Start-Up Accelerators and Their Impact on Entrepreneurship and Social Responsibility of the Manager

Abstract

Startup accelerators are a highly useful part of the entrepreneurial ecosystem. They are responsible for supporting young innovative enterprises with innovative ideas at the early stages of their development. Problems related to building a business model, raising funds for business development, or determining the directions of development of the products and services offered are often just the tip of the iceberg, which can be a serious obstacle preventing survival on the market and achieving commercial success. Accelerators are entities supporting innovation, which, using the tools and programs they have, can significantly facilitate issues related to running a business by immature start-ups and significantly contribute to overcoming the challenges that constantly appear before them. Due to the importance of innovation in the global economy and its obvious connection with start-ups, scientists in the last decade have clearly marked their interest in the subject of start-up accelerators. The purpose of this research work is to present the current state of knowledge in the area of accelerators and to systematize it. For this purpose, a literature review describing issues related to start-up accelerators was reviewed and a bibliometric analysis was carried out. As a result of the research, the topics in the area of accelerators that were most often taken up by scientists and the details on which previous publications focused were shown. The authors hope that the presented study will be valuable material for theoreticians conducting future research on start-up accelerators, and will also be a useful support for practitioners from such entities as start-ups, accelerators, corporations, and government agencies.

1. Introduction

The dynamics of changes currently taking place in the global economy forces enterprises to constantly adapt to the constantly changing environment. What is standard today may be a long-forgotten and inefficient technology tomorrow. The evolution of the global economy is determined by such phenomena as the pursuit of sustainable development, environmental protection and changes in accordance with the assumptions of Industry 4.0. However, it is necessary to take into account the possibility of the emergence of new philosophies, phenomena and technologies that may change the direction in which the world economy is heading. Entrepreneurs must be aware of the pace of change and constantly observe their micro- and macro-environment. In this way, they can gain valuable information about the changes taking place in the environment, learn about the needs of potential customers, and thus give themselves a chance to properly adapt to the changing requirements of the business environment. More importantly, careful observation can lead to the clarification of innovative solutions that will meet market needs. It is innovations that are the driving force of change and one of the main stimuli for generating an advantage over the competition, which defines the company’s position in the business chain. The current functioning of the market indirectly forces enterprises to introduce innovations, because only such activities can guarantee their survival. The market demand for novelties and creative solutions is huge. Entities that very often provide this valuable “resource” are start-ups. These, however, despite having a “breakthrough” solution, often do not have the appropriate knowledge on how to transform their innovation from an idea into a real business. Issues related to launching a product or service on the market or properly presenting it to the client often exceed the capabilities of start-ups. Sometimes an idea possessed by young companies, even though it is interesting and innovative, for some reasons has no chance for effective commercialization and scaling. Start-ups are often characterized by a weaker financial condition and relatively low maturity, which can significantly hinder activities related to introducing a product or service to the market. The answer to such problems are start-up accelerators, which can significantly support the processes of building a business framework for young enterprises. Accelerators can offer assistance on many levels of start-up activity. This may be expert assistance concerning issues in the field of activity of the supported entity, or financial assistance supporting the processes of introducing a new solution to the market. The start-up accelerator should be treated as an intermediary that paves the way for young enterprises to introduce an innovative idea to the market. Different entities can play the role of an accelerator, ranging from mature enterprises that set up their own corporate accelerators in order to seek innovation from the outside, to various types of accelerators fully specialized in building relationships between a corporation and a start-up or between a market and a start-up. Each of the potential parties to the acceleration program has its own motivations, but only their effective cooperation can bring benefits to all parties.

The subject of accelerators and start-ups is becoming more and more popular over time and is more and more often taken up in various research works. Due to the relatively young age of this area of research, it is an unsystematized space and contains some unknowns, as indicated by individual authors in their publications [1,2,3].

Startup accelerators are a tool supporting the development of new ventures by providing them with capital, knowledge, mentors and connections with potential business partners. Their goal is to increase the chances of a startup’s success by accelerating its development and increasing its market value. In the theoretical context, accelerators are perceived as an element of the startup ecosystem that allows the creation of new innovative enterprises and increasing their growth potential. They are considered an innovative solution that helps overcome market entry barriers and minimize the risk associated with the development of a startup. The theoretical approach to accelerators focuses on the process of accelerating the development of startups by supporting them. Different models of accelerators should be distinguished here, such as corporate accelerators, seed accelerators, industry accelerators or academic accelerators. Each of them has its own characteristics and characteristics that affect the way they help startups in their development. An important theoretical element in the context of accelerators is also their role in the innovation ecosystem. Accelerators create a network of connections between startups, investors, mentors and other enterprises, which contributes to increasing the growth potential of the entire innovation ecosystem. In this way, accelerators play an important role in creating new innovative enterprises and in developing a knowledge-based economy.

This paper is a literature review along with a bibliometric analysis of a specific set of publications in order to obtain an overview of the current state of the art in the topic of start-up accelerators. Research works lead to the systematization of the hitherto achievements of researchers in this field of science. The study of papers published in the Web of Science database in 2011–2021 is characterized by an innovative approach to the analysis of scientific papers for several reasons: systematic literature review and bibliometric analysis is a relatively new method of analyzing scientific publications, enabling researchers to accurately and in detail analyze the impact of scientific publications on a specific field; it allows you to obtain objective scientific results and measures that can be used to compare and assess the quality of scientific publications in a manner independent of the subjective assessments of experts. In addition, the approach used in the paper can help researchers design further research and set new research directions, which will contribute to the development of the area of science analyzed by the authors and the discovery of new scientific knowledge. The result of the conducted research is meeting the expectations of scientists indicating the need for further research and systematization of knowledge in this area.

This paper is a continuation of the research carried out by the authors. The authors believe that the previous studies do not exhaust the subject of the analyzed topic [4,5,6,7,8,9], and the new studies presented in this paper are complementary to the earlier studies. In this work, the authors also used other research methods and present new conclusions that differ from those presented in previous studies.

The publication has the following structure: the first part of the paper is an introduction, then the research methodology is presented, the third part contains a literature review, and the fourth part presents a bibliometric analysis. Conclusions constitute the final part of the paper.

2. Systematic Literature Review

The first of the publications collected for the purposes of the conducted research comes from 2011, it is a report on the activities of the academic accelerator project Syracuse Student Startup Accelerator. This project was located in upstate New York, in a popular academic center in the United States. The publication presents the motivation for initiating such a program, which was mainly due to the desire to ensure optimal development in the field of innovation and entrepreneurship of the studied region. According to experts, it did not sufficiently use the potential of the student community gathered in this area. As a result, a package of actions, tools and suggestions was proposed, the proper implementation and use of which should ensure the expected economic development of the northern part of the state of New York, and was also a proposal for a model functioning of an academic accelerator for other academic communities [10].

Another classified publication dates from 2013. It addresses the topic of start-up survivability depending on the factors determining the acceleration program. The research focused on comparing the survival rates of start-ups from Silicon Valley and Ireland and start-ups cooperating with leading accelerators from other regions of the world. In the course of the research, the main features of the accelerator that affect the survivability of the supported start-up were identified, and the essence of the operation of start-up accelerators was described in detail [11].

In the paper from 2014, it was undertaken to analyze the method of collecting and transferring information and the selection of enterprises for the portfolio of accelerated entities. Considerations regarding the distribution of information indicate that the accelerator may observe signals encouraging early exit from investments, and may also apply a policy of not disclosing negative signals relating to units included in the accelerator’s portfolio [12].

Understanding the factors that lead start-ups to cooperate with accelerators is the essence of the next study from 2015. The purpose of this type of cooperation is to obtain mutual benefits, which take a different form depending on the party. In this case, the research work included an analysis of resources considered necessary from the perspective of start-ups, and in which the accelerator can be helpful. On the other hand, the effectiveness of accelerators in the context of meeting the needs of a start-up and the way in which the desired resources are delivered to the supported party was checked. In addition, the dynamics of changes in the needs of the supported project over time and changes in the stages of its development were examined. The research was based on a review of the activities of two recognized European start-up accelerators. For this purpose, 40 interviews were conducted with participants of acceleration programs [13].

The conference materials from 2015 mention the problem of designing a business model for entrepreneurs who want to enter the market with their innovation. The study presented at that time contains a literature review in a given thematic area, as well as a proposal for a new approach in action-oriented entrepreneurship. This model is based on the assumptions of the discovery-driven approach, but has been adapted specifically to the needs of new and innovative technological ventures that want to commercialize their ideas. As a result, the presented publication offers a new approach that can play a useful role in the design of a business model [14].

The most frequently cited publication among those collected for the purposes of the conducted research deals with the topic of building the right foundations for cooperation between a corporation and a start-up. The author emphasizes that the appropriate design of the acceleration program is a key aspect of cooperation and only a rational approach to project dimensions (proposal, process, people and place) can guarantee mutual benefits. The basis for the research was the analysis of information obtained during interviews with managers and participants of corporate accelerators [15].

In the subject of academic accelerators, interesting observations are offered by a publication that describes the work on the creation and operation of the Open Laboratories of Ideas, Methods and Practices organization, the main goal of which was to facilitate integration between the academic side—in the main mainly students, and centers related to running a business, e.g., start-up accelerators. The paper considers the advantages and disadvantages of establishing cooperation between these parties, with particular attention paid to the mutual interaction of the entities participating in the study. A practical example of such cooperation was the presentation of the cooperation between the established organization and the Student Research Laboratory of Optical Engineering at the ITMO University [16].

Another work is the result of research by the scientific community in Slovakia. Slovak researchers analyzed a case study of a local start-up accelerator and data obtained from known global accelerators. On the basis of research works, the processes taking place in the acceleration program were presented and characterized, and investment criteria for this type of programs were defined [17].

In 2017, the topic of corporate accelerators was developed in two publications. In the first of them, the research work consisted in studying 6 cases of cooperation between a corporation and a start-up and outlining a model form of this relationship depending on the criteria of the goal, necessary investments and commitment of the parties. The authors emphasize the need to construct effective knowledge flow mechanisms between units participating in the acceleration program. In connection with this issue, they proposed the term “Knowledge Effusion” [18].

Research on cooperation between companies with an established and strong market position and start-ups was presented in the next scientific paper. Its main task was to identify problems that disturb the functioning of acceleration processes, and to determine the causes of their occurrence. To this end, the research group conducted 27 interviews with representatives of start-ups, companies with a strong position and the management of acceleration programs. On this basis, it was found that the main factors weakening the strength of cooperation between the examined parties include differences in basic beliefs and incompatibilities appearing at the level of power, autonomy and risk, as well as purely personal and ambitious reasons [19].

The topic of academic accelerators also returns in 2017 thanks to Spanish scientists who presented the European Startup Scaleup project. It was an evolution of the Cloud Incubator HUB run in Spain. Initially, it was a team integrating a group of scientists from the Carthage Polytechnic who dealt with industrial electronics, but over time the initiative expanded to include cooperation with research centers in Dublin, Vilnius and Zoetermeer. The work is a review of experiences from the researched projects and a proposal of good practices for participants of future acceleration programs [20].

Another publication deals with the process of evaluating acceleration programs. Therefore, during the research, the concept of evaluating start-ups at the early stages of their development was proposed. According to the researchers, this will allow for a rational and correct selection of start-ups in which capital and other resources should be invested. For the purpose of the study, the authors of the publication conducted 8 expert interviews, the results of which were extended by an online survey. The proposed concept of assessing start-ups consists of 7 areas of activity that are part of the executive level, management level or ambassador level. The practical application of the concept at the management level was tested in a partnership program between a start-up accelerator and a corporate venture capitalist [21].

Another paper published in 2017 presents organizational issues and problems faced by ICT start-ups that cooperate with healthcare entities. The area of activity related to medicine was described by the authors of the paper as “extremely resistant to radical innovations”. The essence of the research was to collect and analyze data and documents from start-up acceleration programs in the field of healthcare. Based on the research, a theoretical model was presented that describes the concepts of introducing organizational changes during the innovation implementation process. The role of institutional sensitivity in such projects has been emphasized [22].

Research work based on studying a set of data from accelerators allowed for the preparation of another publication. Its purpose was to determine the impact of individual elements and parts of the acceleration program on the value of the fund generated by cooperation with a start-up. The research included an analysis of the business model, the impact of non-financial benefits and their interrelationships. The result of the research was the specification of the key values responsible for the success of the acceleration program [23].

The aim of another study was to compare several types of accelerators based on a research sample collected according to the value of funding collected by start-ups run by them. As a result, the authors of the paper presented their observations on the impact of individual elements of business models on the financial results of the accelerator. An additional value of the publication was the presentation and comparison of non-financial benefits for a start-up resulting from cooperation with the accelerator. The study contains a proposal for an acceleration program depending on financial results [24].

The year 2018 is characterized by a significant increase in interest in the subject of start-up accelerators. Over the course of 12 months, the scope of literature describing issues related to corporate accelerators has been significantly expanded and the concept of seed accelerators has been observed for the first time.

Determining the key factors defining the success of the start-up acceleration process was the main topic of the next study. For the purposes of this study, 12 acceleration processes were analyzed. The first factor indicated was the important role played by the rational design of a differentiated value proposition for start-ups in the context of capitalization of corporate assets. Equally important should be the development of a communication management framework between the corporation and the start-up. The important role that specialists (dedicated business developers) can play, responsible for proper communication between the parties mentioned, is emphasized here [25].

Another publication presents the perspective of the approach to the use of corporate accelerators from the point of view of representatives of the agribusiness industry. Using the experience of the Alltech acceleration entity, a description and analysis of the acceleration process was made, taking into account feedback for the internal team and representatives of the supported start-up. The result of the work was the identification of key areas that should be taken into account when building an optimal acceleration program, especially in the area of agribusiness [26].

The subject of the essence of cooperation between corporations and start-ups is also developed in the next publication. Its aim was to explore the motives that may define such cooperation. In this case, the impact of the directions of development of the 21st century economies, based on the ubiquitous digitization and the accelerated dynamics of innovation cycles, was particularly taken into account. The author points out a certain research gap in the explored area of research, then distinguishes a number of benefits that established corporations can offer to start-ups. The key result of the research was the presentation of 9 basic motives for cooperation between a corporation and a start-up [27].

Considerations regarding the support of innovation by corporations with a strong and established position are the subject of another study. Its authors, based on interviews with representatives of two German technology companies, analyze corporate accelerators, characterize their operating model and assess their impact on the level of innovativeness of the enterprise [28].

The next research work is an analysis and description of how corporate start-up accelerators operate, detailing the organizational structure of acceleration programs and accompanying processes. The research included a review of the available literature, interviews with representatives of both the corporate side and start-ups, and an analysis of the results obtained. The aim of the work was to thoroughly understand the essence of acceleration processes and to learn more about the expectations of both parties regarding the acceleration program [29].

A description of the entrepreneurship and innovation environment in Romania, with a particular analysis of the selection processes of start-ups for acceleration programs and their subsequent evaluation, is presented in the next study. It was based on the analysis of 6 leading start-up accelerators in Romania, and its aim was to identify the characteristics of the local business environment and to propose recommendations to improve the efficiency of local accelerators [30].

The aim of another publication from 2018 was to develop methods for identifying and positioning start-up acceleration and incubation entities. The result of the research was the development of best practices in the field of business ventures and the specification of key indicators describing the system parameters for positioning innovation support entities according to the size of capitalization and other quantitative and qualitative indicators [31].

Another work is characterized by an interesting approach, the idea of which was based on examining the human and social aspects in the context of a start-up accelerator. The aim of the study was to determine the impact of the human aspect on the social aspect, and going further—on the operation of the entire acceleration program. This was achieved by analyzing components such as “know-what” and “know-how”, which are part of human capital, and “know-who”, which is part of social capital. Based on the research, it was found that the previously mentioned components are interrelated, and social capital can provide better means of access to human capital components and improve the level of effectiveness of its use [32].

Yet another paper compares two public acceleration programs: Start-Up Brazil and Start-Up Chile. The mechanisms of both systems were analyzed in search of differences and similarities between them. The result of the research was a confirmation of the positive impact of acceleration programs on investment efficiency, the authors also proposed corrections regarding the functioning of both accelerators [33].

An interesting extension to the paper described above is the study from 2018, which also assessed the Brazilian innovation support program—the aforementioned Start-up Brazil. This item is an overview, analysis and description of the accelerators included in this project. Its effect was to classify accelerators according to specific criteria, such as the profile of start-ups selected by accelerators, information about the accelerator (place of acceleration, number of acceleration programs run), etc. [34].

The next study analyzes the increasingly exploited approach in which companies with a strong market position try to increase the effectiveness of their two-way activities. These are activities focused on nurturing and leveraging current lines of business, and activities on discovering and developing innovations. The research work includes a comparison of the forms of increasing the level of innovation in connection with three different acceleration programs [35].

Another publication deals with the problem of the location of particular types of accelerators in the process of development of enterprises and the entire entrepreneurial ecosystem. The research work covered 3 distinguished subsystems of the entrepreneurship environment and the presentation of the model role of the accelerator in relation to the entrepreneurship ecosystem. Using the Pipeline model, the location of the accelerator in the entrepreneurial environment was outlined, and then the characteristics of individual types of accelerators were presented with the presentation of how they can support participants in the acceleration program. The publication can be used by practitioners to optimize management processes and organize acceleration programs using the entrepreneurship ecosystem [36].

Another study brought together 3 publications by a Spanish group of scientists affiliated with the University of Valencia (Canovas-Saiz, March-Chorda, Yague-Perales). All of their identified works cover topics related to the concept of the seed accelerator. The first was published in 2018 and addressed the social impact generated by seed accelerators. For this purpose, the number of new jobs created by undertakings participating in acceleration programs was analysed. The study allowed to identify the key properties responsible for generating employment in start-ups supported by seed accelerators, which is a useful source of information for public and private entities interested in supporting the development of innovation and entrepreneurship [37].

In the publication of other authors referring to the subject of the seed accelerator, they attempt to familiarize themselves with the method of selecting start-ups for the implementation of acceleration programs based on the analysis of data from the accelerator located in Southeast Asia. The primary objective of the research was to determine the key decision criteria related to the start-up selection process. The real-win-worth criterion analysis model, consisting of 30 different criteria, was used for the purposes of the research work. The result of the research was the identification of key criteria in the process of initial selection and the final selection of start-ups. In addition, regression models have been proposed for the criteria considered key, allowing to improve the effectiveness of the selection of start-ups participating in acceleration programs [38].

The year 2019 should be considered the most fruitful when it comes to the subject of start-up accelerators and related issues. As many as 15 out of 56 completed studies from the Web of Science database have been published this year. The leading topics were to deepen knowledge in the field of the functioning of accelerators, as well as start-ups. At the same time, there were also many publications describing the operation of corporate, seed and academic accelerators.

One of the papers presents research work on corporate accelerators in the context of their different types. The research was based on conducting interviews with representatives of 16 leading German corporate accelerators, and then analyzing the obtained data. The result of the research was the indication of 5 types of accelerators that have their own characteristic features in strategic, organizational and process aspects [39].

Another publication sheds an interesting light on the essence of corporate accelerators. Its purpose was to examine the motives for establishing corporate accelerators and the characteristics of activities during the design and implementation of the acceleration program. As a result, the acceleration processes were decomposed into prime factors, and two key ways defining the way of managing a corporate accelerator were specified. One focuses on accelerating the strategic adjustment, while the other leads to accelerating the creation of the enterprise—it depends on the adopted strategy and the time horizon of the investment [40].

In the next publication, the authors analyze secondary data and information obtained on the basis of interviews conducted with participants of acceleration programs. The aim of the work was to distinguish types of corporate accelerators and to indicate the characteristics that define a given type. The creation of such a classification is a valuable information material for the management of the acceleration program. It can be used to prepare the correct strategy and framework for cooperation between the corporation and the start-up [41].

Another publication presents the general characteristics of the innovation environment in Portugal. The analysis was carried out in terms of determining the overall level of innovation, propensity to open innovation and sustainability of projects. The research work was based on the use of the HJ-Biplot methodology for Social Innovation Survey (CIS) data in Portugal. As a result of the research, it was indicated that Portuguese companies support and maintain activities that do not lead to the expected results. The solution is to establish appropriate relations with business partners (e.g., start-up accelerators) who, with their capital and knowledge, can significantly improve the innovativeness of the country. This is achieved through more effective implementation and maintenance of acceleration programs for start-ups. This is especially important in the context of increasingly popular trends in entrepreneurship, such as smart cities and Industry 4.0 [42].

The analysis of start-up accelerators and crowdfunding in the context of entrepreneurship in Thailand is the subject of the next study. The study in particular referred to accelerators supporting the commercialization of innovations and the eco-innovation system of start-ups. On its basis, it was determined that the triple helix system—the interaction between universities, industry and government—is disturbed, which limits the country’s innovative capacity. The authors emphasize that acceleration programs include the use of useful tools and activities that can fix and improve the aforementioned interaction [43].

The aim of another publication was to identify the key factors in the context of the success of the acceleration program. As a result of reviewing and analyzing the literature related to the subject of open innovation, the authors define reputation, co-creation and establishing cooperation as key factors determining the success of a start-up. An additional value of the research work is the indication of the configuration elements of the acceleration program and the determination of their impact on the above-mentioned factors [2,44].

Another work is an analysis of acceleration programs in terms of their impact on international entrepreneurship. The foundation of the research work presented there was a detailed analysis of data from projects of one start-up accelerator. The positive role of accelerators, which assume the role of intermediaries strengthening the connections and relational networks of the start-up with the environment, was emphasized. At the same time, the authors of the paper express doubts whether adopting a similar form of supporting innovation by public institutions is the correct solution—in their opinion, problems related to supporting innovation in this way may appear in weaker entrepreneurship ecosystems [45].

The authors of the next publication point to the increasingly important role of acceleration programs in supporting entrepreneurship. Therefore, they attempted to explain the differences between the assumptions of individual acceleration programs and their results. The study includes an analysis of acceleration programs starting from the stages of their design. The authors of the publication are looking for correlations between specific elements of the program and the subsequent result of cooperation between the accelerator and the start-up. The effect is to analyze the impact of the project on the subsequent performance of the program and to present differences in the approach to running accelerators [46].

The basis of another research work was the creation of a panel composed of participants of meetings held as part of an international start-up accelerator. The aim of the research was to determine the impact of contracting capacity and institutional distance when making decisions about insourcing and outsourcing. As a result, it was found that the studied factors affect the project management strategy and the assessment between transaction and bureaucratic costs for a start-up. The difference in decision-making towards a start-up depending on whether these are national or international projects was also emphasized [41,47].

Another research paper proposes an interesting approach. It was based on a comparison of 4 case studies of start-ups from the cleantech industry: 2 cases of projects supported by start-up accelerators and 2 cases developed without such support. The research work consisted in analyzing these 4 start-ups in the context of the speed of starting operations, access to the network of resources and the efficiency of their use, and catching up by the start-up. These three mechanisms are responsible for shortening the time to market and proper organization and management of the project. The authors of the paper proposed the concept of the minimum profitable start-up as an extension of the concept of the minimum profitable product in the context of accelerator activities [48].

Another publication explores the territorial context in the entrepreneurial environment and the correlation between knowledge flow processes and ‘location on the map’. Entrepreneurship in digital fields has been included in the scope of research work, noting that there is currently insufficient appreciation of digitization in the context of knowledge flow. The basis of the research is a review and analysis of accelerators from 4 cities: German Berlin and Hamburg, American Detroit and Dutch Amsterdam. According to the authors of the paper, it is a mistake to analyze the entrepreneurial ecosystem within rigid geographical boundaries. Thus, they suggest that entrepreneurship is not rigidly embedded in a given region, but is based on supra-regional resources. The publication contains a proposal to extend the territorial analysis with the concept of topological view [49,50].

The topic of start-up accelerators in academic terms reappears in 2019. One of the publications presents the development of an academic accelerator founded in Austria in cooperation with two universities from Graz. In its initial phase, it was a non-obligatory course project where students with interesting ideas could get guidance from university theorists and business representatives. Over time, the positively received program evolved and took the form of a fully professional academic start-up accelerator. The research paper is an overview and report of a program that is an example of a well-complementary model of cooperation between the university, its creative student base and business [51].

Another work on academic accelerators presents a model functioning of an entity of this type. The added value of the work is the presentation of how to classify the degree of digitization of a start-up. The author presents several projects with examples of their classification and formulates suggestions for future research in this area [52]. The next publication is an analysis of the operation of the university accelerator, with particular emphasis on examining the entrepreneur-coach relationship in the context of the rapidly developing lean startup methodology. It was examined how the role of the coach can interact with the given methodology. As a result, the evolutionary impact of the researched methodology on the relationship between the company and the mentor was noticed, and it was noted that the relationships formed in this way facilitate the learning process among entrepreneurs. The emerging conflict between the coach’s position and the information obtained from clients was also emphasized. This was due to the fact that trainers were often perceived as leaders whose opinions were valued more than the data obtained, which is contrary to the fundamental theory of the lean startup methodology [53].

In 2019, an interesting paper was also published in which the subject of accelerators was discussed with an interesting research background, which is the development of a metropolitan center on the example of the Silesian Metropolis. The important role played by start-up accelerators and other entities supporting the development of innovation in the process of building a healthy and modern business environment was emphasized. The authors of the work pay great attention to the issue of diversity among accelerators. The basis of the work is to discuss the essence of accelerators in accordance with the configuration approach, based on three main assumptions: the concept of the ideal type, the concept of “matching” and the concept of equality. The effect of the work is to propose and explain 5 functional-structural pairs according to which accelerators can be categorized [54]. In 2020, we observe a significant decrease in the involvement of the scientific community in research on start-up accelerators. This is probably related to the outbreak of the COVID-19 pandemic, which redefined the priorities of scientists and business representatives, and also hindered communication, which is often an important element of research work.

An interesting observation is presented in a publication in which the functioning of corporate accelerators was examined from a psychological point of view. Based on the analysis of 10 cases of acceleration programs from two corporations, comments on cooperation between a corporation and a start-up were presented. The authors divided the acceleration program into three phases, and in each of them they identified a different dominant emotional state (hope, fear, acceptance). In addition, the publication contains a presentation of a number of behavioral reactions that are the response of program participants to subsequent emerging challenges [55].

The context of the lean startup methodology returns in another publication from 2020. This time the issue of learning by doing was examined. Based on the data obtained during the analysis of 152 cases of cooperation with the American program to support lean startups, it was noticed that the key elements of the method—formulating hypotheses, probing and convergence of ideas—combine as expected. In addition, it was noticed that educated managers, despite initial objections to the use of the method, over time appreciate its value. In addition, it was found that due to the high universality of the lean startup methodology, its assumptions are often tested insufficiently rigorously, without taking into account critical boundary conditions. The added value of the work is the indication of the level of education and knowledge in the field of business management of the project team as a critical boundary condition for the use of lean startup. Based on the research results, the authors of the publication inform that within 18 months after the introduction of the methodology, an improvement in the company’s results is noticeable [47]. In another paper, observations on seed accelerators were presented, focusing on the essence of the presence of the accelerator in the environment of a growing company. The research involved analyzing seed acceleration programs as schematic sequences of physical co-presence. Their effect was to distinguish 8 forms of physical cooperation between the accelerator and the start-up. The role of the proposed forms of physical presence in the process of nurturing unique social dynamics between the entities of the acceleration program was emphasized. It was pointed out that by rationally designing the sequence of events and appropriate combination of presence and absence situations, a process with a higher probability of achieving the expected result by the acceleration program is created [56].

In 2020, a group of Spanish scientists from the University of Valencia once again focused on the topic of seed accelerators. Emphasizing the important role of this form of innovation support, they conducted relevant research and made a detailed assessment of the accelerator’s impact on the functioning of the surrounding entrepreneurship ecosystem. The foundation of the research was the analysis of data obtained during interviews conducted with representatives of 116 seed accelerators. The publication contains a discussion of the research results and helpful suggestions regarding the management of seed accelerators and directions of development of a given research area [57].

In 2021, these authors expanded their research on seed accelerators with one more publication. This time it referred to the topic of analyzing the results and assessing the effectiveness of acceleration programs. To this end, the study included an assessment of the performance of the acceleration program from the perspective of the seed accelerator, as well as an assessment of the prospects obtained by the supported start-up. On this basis, the impact of some factors on the results of acceleration programs for the accelerator and supported companies was characterized [58].

In 2020, a paper was published based on the analysis of an academic accelerator established at one of the universities in Egypt. It has been enriched with research on the literature in this field. As a result, a model acceleration program was developed, which can be a practical aid in later acceleration processes. The proposed model contained a proposal for the process of designing, monitoring and adjusting the program depending on the characteristics of the case. In addition, the author created a set of parameters that may allow for easier determination of the aforementioned characteristics of the case [59].

The next paper presents observations on the model supplementing the hitherto popular forms of cooperation between corporations and start-ups. As the authors of the study noted, more and more often the processes of searching for and supporting innovations are part of the strategic activities of companies with an established market position. The publication includes an analysis of data from acceleration programs, an indication of the reasons for their initiation and identification of key elements of the acceleration program. In addition, the authors present valuable suggestions for the effective implementation of acceleration projects [60].

The year 2021 brings a revival in the area of research on accelerators. In terms of the number of published studies on this topic, the result from the previous year was equalized already in the middle of the year, so there is a high probability that at the end of 2021 this number will refer to the results from 2018–2019.

In addition to the above-mentioned study on seed accelerators, in 2021 the topic of corporate accelerators was also examined, focusing on the challenges that the accelerator faces during the acceleration programs. According to the authors, the motivation to undertake such a topic was, according to the authors, insufficient presentation of the topic in the existing literature. For the research work, 28 semi-structured interviews were conducted with innovation experts in various sectors. The result of the research was the presentation of a package of guidelines for representatives of accelerators, which concern the increase in the effectiveness of organizational learning and the efficiency of an innovative corporation [1,61].

In another study devoted to corporate acceleration programs, the authors attempted to identify the motives leading to the establishment of this type of cooperation to support innovation. During the research, they distinguished the main benefits and challenges related to running an accelerator. The basis of the scientific work was the use of in-depth interviews (IDI) with participants of acceleration programs and conducting a focus interview with a group of experts in this field. The research was enriched with the analysis of secondary data. As a result, the positive impact of the activities of corporate accelerators on the level of innovation development was confirmed [62].

Another publication deals with the presentation of the activities of the Israeli research and development unit MindCET, which successfully conducts i.a. start-up accelerator. The research work included the study of data from two years of the activity of the surveyed organization together with the analysis of the collected interviews and publications. The aim of the author was to develop conclusions regarding the relationship between reforms in the education system and educational technologies [63].

The set of analyzed publications also included a study created from the need to improve the economic situation of Nigeria. The author, encouraged by the results of previous research, assumed that the accelerator in the general sense is an achievable form of activity that can guarantee sustainable development. To this end, he analyzed previous studies and cases of the operation of accelerators from Silicon Valley. Its purpose was to identify the factors affecting the efficiency of the acceleration program. During the research, the theory of “sustainable start-up growth” was proposed and tested, based on the hypothesis that the quality of the services offered is superior to the number of projects carried out by accelerators. In addition, it was found that the sectoral concentration of the accelerator is an important factor influencing the final result of the activities. The result of the research was the confirmation of the hypothesis [64]. The last publication classified for the purposes of this study indicated that there are 4 mechanisms explaining the essence of the operation of accelerators. The paper highlights the existing research gap in the subject of accelerators [3,65].

Based on the analysis of the collected publications on the subject of start-up accelerators, we can observe the trends that have prevailed in this area of research over the last decade. It should be emphasized that in the years 2011–2015 it was a niche topic and overlooked in scientific publications. A clear increase in interest in it occurred in the second half of the analyzed period. This is related to the increased awareness of theoreticians and practitioners in terms of understanding the usefulness of accelerators. The value of this form of supporting innovation has been appreciated, especially since the increase in the level of innovation has a direct impact on economic growth and the general level of entrepreneurship.

Accelerators have a wide range of tools thanks to which they can significantly support the activities of developing start-ups at various stages of their development, starting from the transfer of knowledge, tips and suggestions regarding various levels of operation of the venture, various forms of mentoring, going through specific cooperation during the design framework for the operation of the project, and ending with direct financial support [66,67]. It is important to consciously build a relationship between the accelerator and the start-up, because only in this way is it possible to achieve joint success [68,69]. The start-up must be aware of the expectations of the supporting entity and realistically assess the chances of successful cooperation. In the period 2011–2021, scientific papers on start-up accelerators clarified many issues related to the topic we studied. The essence of the functioning of various types of accelerators and start-ups was widely presented, the scope of designing and functioning of acceleration programs and the motives for establishing cooperation of this type were presented, methods of selecting start-ups and subsequent evaluation of acceleration programs were proposed. The concepts of, among others, corporate, academic and seed accelerator.

3. Materials and Methods

The aim of the paper is to present and systematize the current state of knowledge about start-up accelerators. For the purposes of the study, the following question was asked: What is the current state of knowledge on the subject of start-up accelerators?

In order to achieve the set goal, two research methods were used:

• Systematic literature review,
• Bibliometric analysis.

The combination of the above methodologies allowed to obtain a wide range of knowledge on the subject under study. Their implementation consisted of:

• Systematic review of the literature—the authors of the study undertook to analyze the current scope of knowledge on the subject of start-up accelerators. For the purposes of the research, the Web of Science database was selected, in which publications from the years 2011–2021 were searched for containing the words “startup accelerator” and its synonyms in titles, abstracts and keywords. On this basis, 60 publications were collected and analyzed in detail. As a result, the final number of papers was reduced so that they were fully related to the purpose of the research. At this stage, 4 papers were rejected due to their incompatibility with the subject of the study and the criteria for inclusion in the analysis, and the lack of sufficient substantive and methodological quality. Finally, 56 publications on start-up accelerators were classified.
• Bibliometric analysis—this stage of the research consisted in analyzing 56 publications collected in the Web of Science database, which are closely related to the topic of start-up accelerators. The bibliometric analysis was aimed at organizing the collected material, taking into account the following factors:

• continents and countries involved in research on the topic of start-up accelerators;
• sources of publications involved in research on the topic of start-up accelerators;
• authors involved in research on the topic of start-up accelerators;
• research units involved in research on the topic of start-up accelerators.

In addition, at this stage of the research, the following parameters were defined for the previously defined factors:

• the average citations per paper (TC/TP), which was determined on the basis of the total number of papers (TP) and the total number of citations (TC);
• indicator-based analysis, in which it was used ij—the impact factor of the analyzed research topic calculated for the j-th source, Pearson’s and correlation $c_p^Y$—weighted coefficient of the number of citations per year in the p-th publication.

4. Results—Bibliometric Analysis

The first publication on the subject of start-up accelerators was published in the Web of Science database in 2011 [10]. In the years 2011–2014, three papers were classified in this area of research: one item in 2011, 2013 and 2014 [10,12,70]. The year 2015 marked the beginning of an increase in interest in this topic–two studies were published [66,67]. In the following years, this trend gained momentum and 3, 7, 14 and 15 papers appeared in succession. In 2020, we can observe a decrease in the involvement of scientists in exploring this area of science, resulting in the appearance of only 6 papers [71,72]. This is probably related to the COVID-19 pandemic and its impact on scientific activity—a change in research priorities and communication difficulties. By the end of August 2021, 6 publications were classified, which is a good omen for the community interested in deepening knowledge in the field of start-up accelerators. Figure 1 presents the number of publications published in 2011–2021.

The next area of analysis is to check the geographic context of research on start-up accelerators. Continents and countries from which their authors come are analyzed.

Table 1. Continents—productivity.

Rank	Continent	TP	TC	TC/TP	Rank	Continent	TP	TC	TC/TP
1	North America	15	217	14.47	4	Australia	3	32	10.67
2	Europe	49	195	3.98	5	South America	4	13	3.25
3	Asia	5	37	7.4	6	Africa	1	0	0

Source: own elaboration.

presents the continents from which the authors of publications dealing with the topic of start-up accelerators come from. For the purposes of this stage, an analysis of the total number of publications (TP), total number of citations (TC) and the ratio of these two parameters (TC/TP) was carried out.

The continent from which the authors prepared the largest number of publications on the topic of start-up accelerators is Europe, however, researchers from North America can boast of the largest number of citations of their publications. In Europe, 49 papers were published and cited 195 times, resulting in 3.98 citations per paper. The result of Europe consists of the work of scientists from 17 countries. Another continent with an important role in research on the topic of start-up accelerators is North America, which is represented only by researchers from the United States. 15 papers were published there, which were cited 217 times, which in effect translates into 14.47 citations per paper. The papers of researchers from Australia and Asia have a high ratio of the number of citations to the number of publications, with values of 10.67 and 7.4, respectively [73,74].

Table 2. Countries—productivity.

Rank	Country	TP	TC	TC/TP	Rank	Country	TP	TC	TC/TP	Rank	Country	TP	TC	TC/TP
1	United States	15	217	14,467	11	Chile	2	13	6.5	21	Russian Federation	1	2	2
2	Germany	8	43	5375	12	Denmark	2	8	4	22	Bulgaria	1	1	1
3	Australia	3	32	10,667	13	Finland	2	8	4	23	Poland	3	1	0.33
4	Norway	2	23	11.5	14	Singapore	1	8	8	24	Slovakia	3	1	0.33
5	France	3	21	7	15	Romania	2	6	3	25	Ukraine	1	1	1
6	India	1	21	21	16	Israel	1	5	5	26	Brazil	2	0	0
7	Scotland	2	21	10.5	17	Spain	4	4	1	27	Egypt	1	0	0
8	England	3	18	6	18	Austria	5	3	0.6	28	Latvia	1	0	0
9	Sweden	2	18	9	19	Pakistan	1	3	3	29	South Korea	1	0	0
10	Switzerland	2	14	7	20	Portugal	2	2	1

Source: own elaboration.

presents the countries from which the authors of publications dealing with the topic of start-up accelerators come from. For the purposes of this stage, an analysis of the total number of publications (TP), total number of citations (TC) and the ratio of these two parameters (TC/TP) was carried out.

In the collection of publications on the topic of start-up accelerators, 29 countries participating in research on this topic were distinguished. The most productive country in this area of research is the United States, where 15 papers were published and cited 217 times. This results in 14,467 citations per publication. Germany is the next country actively involved in research on this topic. Researchers from this country published 8 papers that were cited in 43 other papers. This gives 5375 citations per paper. Scientists from Australia addressed the topic in 3 publications, which were cited 32 times (TC/TP = 10,667). Other countries with a high citation to published text ratio are: India (21,000), Norway (11,500), Scotland (10,500), Sweden (9000), Singapore (8000), France (7000) and Switzerland (7.00).

Based on research into the productivity of continents and countries, the authors of this paper are inclined to conclude that the location of research on start-up accelerators is related to the level of wealth and economic development of a given region. The United States is the leader in research, being at the same time a pioneer in exploring this topic—the first non-American publications on it appeared in 2015. The United States is the largest and one of the most modern economies in the world, and its start-up market is the largest in the world. This is due to the relatively high (greater than in other regions of the world) knowledge of the topic of start-up accelerators and a greater understanding of the potential behind the process of investing in innovative projects. A similar situation is taking place in Europe, where the unquestionable research leader is Germany, which is the strongest economy of the Old Continent.

The analysis of classified publications devoted to start-up accelerators made it possible to specify the thematic scope of selected works. Of the 56 collected publications, most (18) focus on the general analysis and presentation of the concept of start-up accelerators. The issue of corporate accelerators is presented in 15 publications. The topics of academic accelerators (and seed accelerators (7 papers each) were also studied). Other publications focus on presenting newly developed concepts related to start-up accelerators, or focus on presenting many types of accelerators.

Classified publications were published in 50 sources. In 6 sources, 2 publications were published, and in the remaining cases, 1 publication was published. Source materials include journals, books and conference materials.

Table 3. Sources—productivity.

Rank	Source	TP	TC	TC/TP	Rank	Source	TP	TC	TC/TP
1	Business Horizons	2	100	50	26	Zeitschrift fur Wirtschaftsgeographie	1	2	2
2	Research Policy	1	28	28	27	2017 IEEE 26th International Symposium on Industrial Electronics (ISIE)	1	1	1
3	Journal of Corporate Finance	1	23	23	28	Baltic Journal of Economic Studies	1	1	1
4	Journal of Business Venturing	1	21	21	29	Basiq International Conference: New trends in sustainable business and consumption 2018	1	1	1
5	European Planning Studies	1	16	16	30	California Management Review	1	1	1
6	Creativity and Innovation Management	1	15	15	31	Ciriec-Espana Revista de Economia Publica Social y Cooperativa	1	1	1
7	Technovation	1	13	13	32	Entrepreneurship and Regional Development	1	1	1
8	Asia Pacific Business Review	1	11	11	33	European Journal of Management and Business Economics	1	1	1
9	Journal of Technology Transfer	2	21	10.5	34	International Entrepreneurship and Management Journal	1	1	1
10	IEEE Transactions on Engineering Management	1	8	8	35	Proceedings of The 10th European Conference on Innovation and Entrepreneurship (ecie 2015)	1	1	1
11	Strategic Entrepreneurship Journal	1	7	7	36	Economic and Social Development (ESD)	2	1	0.5
12	Journal of Business Research	1	6	6	37	International Journal of Engineering Pedagogy	2	1	0.5
13	Journal of Service Management	1	6	6	38	2017 IEEE European Technology and Engineering Management Summit (E-TEMS)	1	0	0
14	2018 IEEE International Conference on Engineering, Technology and Innovation (ICE/ITMC)	1	5	5	39	3rd World Multidisciplinary Civil Engineering, Architecture, Urban Planning Symposium (WMCAUS 2018)	1	0	0
15	Learning, Media and Technology	1	5	5	40	Academic Entrepreneurship and Community Engagement: Scholarship in action and the Syracuse miracle	1	0	0
16	Triple Helix	1	5	5	41	African Journal of Science Technology Innovation & Development	1	0	0
17	Entrepreneurship Research Journal	2	8	4	42	Economic and Social Development	1	0	0
18	International Food and Agribusiness Management Review	1	4	4	43	Journal of Organizational Change Management	1	0	0
19	International Journal of Innovation management	2	6	3	44	Journal of Private Equity	1	0	0
20	Research-Technology Management	1	3	3	45	New Challenges of Economic and Business Development—2019: Incentives for Sustainable Economic Growth	1	0	0
21	Ideas in Marketing: Finding The New and Polishing The Old	1	2	2	46	Proceedings of The International Conference on Engineering, Science, and Industrial Applications (ICESI 2017)	1	0	0
22	International Journal of Innovation and Learning	1	2	2	47	Raumforschung und Raumordnung-spatial Research and Planning	1	0	0
23	Optics Education and Outreach IV	1	2	2	48	Revista Eletronica de Estrategia e Negocios—REEN	1	0	0
24	Proceedings of The 8th European Conference on Innovation and Entrepreneurship, vol. 2	1	2	2	49	Revista Geintec-Gestao Inovacao e Tecnologias	1	0	0
25	R & D Management	1	2	2	50	Technology Entrepreneurship: Insights in new technology-based firms, research spin-offs and corporate environments	1	0	0

Source: own elaboration.

shows all sources and contains information on the total number of publications (TP), total number of citations (TC) and the ratio of these two parameters (TC/TP).

The distinguished sources are characterized by a wide range of areas included in the research. Often one publication is related to many different fields of science. The following research areas emerged during the research: Economics and business (40 publications), technical sciences (10), education and educational research (5), public administration (4), geography (3), science and technology (2), urban planning (2), agriculture (1), architecture (1), environmental science and ecology (1), operations research and management science (1), library science (1), optics (1) and development studies (1).

The publications collected for the purposes of the study were cited 334 times. The source with the highest ratio of the number of citations to the number of published publications is Business Horizons. In this scientific journal focusing on business aspects, 2 papers were published, which were cited 100 times [69,72]. Business Horizons is a source with a CiteScore of 11.3 and an Impact Factor of 6.361. Another important source is the “Research Policy” magazine, which published 1 paper cited 28 times [21]. The journal has a CiteScore of 11.4 and an Impact Factor of 8.11. The next position is taken by the “Journal of Corporate Finance” magazine with a CiteScore of 4.9 and an Impact Factor of 4.249. One paper was published in this journal and received 23 citations [18]. Other noteworthy sources are the “Journal of Business Venturing” and “European Planning Studies”, which published one paper each, which received 21 and 16 citations, respectively [27,44].

The 56 collected publications on start-up accelerators were written by 131 authors; The vast majority of them are collective works, only 9 papers were written individually [18,33]. The authors with the highest productivity (3 publications each) are M. Rostarova [17,23,24], whose works have been cited once, and a team of closely cooperating Spanish scientists: L. Canovas-Saiz, I. March-Chorda and R. M. Yague-Perales, whose publications have been cited 3 times [37,57,58]. The author with the highest number of citations is T. Kohler, whose one classified paper was cited 87 times [15].

Table 4. Authors—productivity.

Rank	Author	TP	TC	TC/TP
1	Kohler T.	1	87	87,000
2–5	Cohen S., Fehder D.C., Hochberg Y.V., Murray F.	1	28	28,000
6–7	Kim J.-H., Wagman L.	1	23	23,000
8–9	Jackson P., Richter N.	2	21	10,500
10–11	Shankar R.K., Shepherd D.A.	1	21	21,000
12–17	Brown R., Lee N., Mangematin V., Mawson S., Peterson L., Stayton J.	1	16	16,000
18	Schildhauer T.	1	15	15,000
19–20	Kurpjuweit S., Wagner S.M.	2	14	7000
21–26	Fink A.A., Herstatt C., Karlsson T., Lundqvist M., Mansoori Y., Moschner S.-L.	1	13	13,000
27–30	de Zubielqui G.C., Jones J., Oppelaar L., Seet P.-S.	1	11	11,000
31–35	Kher R., Luo J., Lyons T.S., Yang S., Yin B.	1	8	8000
36–37	Katila R., Leatherbee M.	1	7	7000
38–40	Bustamante C.V., Fuglsang L., Wallin A. J.	1	6	6000
41–51	Alange S., Baltes G.H., Beleiu I.N., Bordean O.N., Bunduchi R., Crisan E.L., Gasser T., Ramiel H., Salanta I.I., Selig C.J., Steiber A.	1	5	5000
52–54	Connolly A.J., Potocki A.D., Turner J.	1	4	4000
55–57	Ben Mahmoud-Jouini S., Duvert C., Esquirol M.	1	3	3000
58	Canovas-Saiz L.	3	3	1000
59–60	Ibert O., Kuebart A.	2	2	1000
61–62	March-Chorda I., Yague-Perales R.M.	3	3	1000
63–79	Beck S., Bhatli D., Bodrov K., Borella P., Castela G., Fernandes S., Heiden C., Hubert M., Ivashchenko M., Jelassi T., McHugh P., Prexl K.-M., Pruegl R., Saillant N., Tolstoba N., Whipple C., Yang X.	1	2	2000
80	Rostarova M.	3	1	0.333
81–84	Alonso D., Ceausu I., Glinik M., Iborra A.	1	1	1000
85–97	Ionescu R., Olaru M., Pastor J.A., Pikalov Y., Rentkova K., Ruseva R., Ruskov P., Ryabokon M., Sanchez P., Suarez T., Tohanean D., Urbaniec M., Zur A.	1	1	1000
98	Janac J.	2	0	0.000
99–131	Ali N., Barbosa da Cruz C.A., Branagan S., de Aragao Gomes I.M., D’Eredita M.A., dos Santos P.R., Gebczynska M., Gfrerer A., Gillig H., Grilo A., Harris W.L., Heinz R., Hutter K., Ismail A., Jung S., Kwiotkowska A., Lindner B., Maldaner L.F., Mealha T., Mendonca V.M., Obloj K., Paixao A.E., Poandl E.M., Schausberger M., Shenkoya T., Soares Silva A.L., Stephan Y., Wasowska A., Wiercinski S., Wojcik P., Wonglimpiyarat J., Zortea C.G.C., Zutshi A.	1	0	0.000

Source: own elaboration.

shows all authors. For the purposes of this stage, an analysis of the total number of publications (TP), total number of citations (TC) and the ratio of these two parameters (TC/TP) was carried out.

96 research units participated in the creation of 56 publications collected for the purpose of examining the current state of knowledge in the field of start-up accelerators. In the case of 27 publications, 1 research center participating in their preparation was indicated. Other works were developed in cooperation with representatives of several research units. The largest number of research units (6) was associated with the development of publications [25]. Most of the awarded research units come from the academic community.

Table 5. Research units—productivity.

Rank	Research Units	TP	TC	TC/TP
1–2	Hawaii Pacific University, University of California, Berkeley	1	87	87
3	University of Innsbruck	2	87	43.5
4	Massachusetts Institute of Technology (MIT)	3	36	12
5	Edith Cowan University	3	32	10.6
6–9	National Bureau of Economic Research, University of Georgia, University of Southern California, University System of Georgia	1	28	28
10–12	Illinois Institute of Technology, University of Colorado Boulder, University of Colorado System	1	23	23
13–15	Entrepreneurship Development Institute of India, Nord University, University of Notre Dame	1	21	21
16	Chalmers University of Technology	2	18	9
17–23	London School of Economics and Political Science, University of London, University of St Andrews, University of Stirling, California State University System, Grenoble Ecole Management, Sonoma State University	1	16	16
24	Alexander Von Humboldt INST Internet Soc	1	15	15
25	ETH Zurich	2	14	7
26	Hamburg University of Technology	1	13	13
27–29	Community Living Australia, Flinders University South Australia, University of Adelaide	1	11	11
30–33	Singapore University of Technology and Design, Baruch College CUNY, City University of New York CUNY System, Michigan State University	1	8	8
34–35	Pontificia Universidad Catolica de Chile, Stanford University	1	7	7
36–39	Alexander von Humboldt INST Internet Gesell, Roskilde University, VTT Technical Research Center Finland, Universidad Adolfo Ibanez	1	6	6
40–45	HTWG University of Applied Sciences, Ben Gurion University, MENLO COLL, Babes Bolyai University from Cluj, University of Edinburgh, University of Rochester	1	5	5
46	Alltech inc.	1	4	4
47–52	Babson College, HEC, New York University, ORANGE, ORANGE San Francisco, ORANGE STARTUP ECOSYST DIV	1	3	3
53	University of Valencia	3	3	1
54–64	Aarhus University, Copenhagen Business School, NOFIMA, OPEN INNOVAT SCI CTR, Zeppelin Univ, BORO OY, Ecole des Ponts ParisTech, Universite Gustave Eiffel, Universite Paris EST Creteil val de Marne UPEC, University of Warwick, Universidade do Algarve	1	2	2
65–66	Brandenburg University of Technology Cottbus, Leibniz Institut IRS	2	2	1
67–68	ITMO University, Brown University	1	2	2
69–70	University of Sofia, Cracow University of Economics	1	1	1
71	Comenius University Bratislava	3	1	0.33
72–79	Bucharest University of Economic Studies, Cherkasy State Technological University, Ministry of Education and Science of Ukraine, Nongovt Org Noosphere, Fac Econ, BluSpecs, Universidad Politecnica de Cartagena, ABB	1	1	1
80	Graz University of Technology	2	1	0.5
81–96	Universidade NOVA de Lisboa, Wexelerate GmbH, Kozminski University, University of Warsaw, Salzburg University, Ferchau ENGN GmbH, Strascheg Center for Entrepreneurship, University of Munich, Universidade do Vale do Rio dos Sinos Unisinos, University of Latvia, Chungnam National University, Syracuse University, American University Cairo, Egyptian Knowledge Bank EKB, Universidade Federal de Sergipe, Silesian University of Technology	1	0	0

Source: own elaboration.

presents all classified test units. The total number of publications (TP), the total number of citations (TC) and the ratio of these two parameters (TC/TP) were analysed. The centers associated with the largest number of publications include: Massachusetts Institute of Technology MIT, Edith Cowan University, University of Valencia and Comenius University Bratislava—representatives of these research units wrote 3 publications each. Publications related to MIT and Edith Cowan University additionally generated a relatively high number of citations: 36 and 32, respectively. citations. All these units are related to the most frequently cited paper from the set of analyzed publications [15].

5. Results—Indicator-Based Analysis

Quantifying the impact of sources and publications contained in the collection obtained from Web of Science, and then extracting the best of them, necessitated the use of ratio analysis [50,75]. It is distinguished by an extended treatment of commonly used indicators, going beyond calculating the trivial ratio of the number of citations to the number of publications or selecting records with the number of citations above a certain threshold (e.g., the Hirsch index [76]). In its case, constants concerning the set as a whole, or the period of publication availability, are involved in the calculations. Therefore, this approach will be incorporated into this work and revised for its adaptation. Minor mistakes in the explanation of the method and its mathematical notation have been removed. In order to ensure the comparability of the improvements, the same markings and the form of presenting the results as in the source material were adopted [67].

The analyzes started with source data. Using Equations (1)–(5), the values of their impact indicators $i_j$ were determined, which, together with the values used in the accounts, are presented in

Table 6. Sources—productivity—additional analysis.

J	Source	${\mathit{c}}_{\mathit{j}}$	${\mathit{p}}_{\mathit{j}}$	${\mathit{i}}_{\mathit{j}}^{\mathit{c}}$	${\mathit{i}}_{\mathit{j}}^{\mathit{p}}$	${\mathit{i}}_{\mathit{j}}$	${\mathit{S}\mathit{N}\mathit{I}\mathit{P}}_{\mathit{j}}$	${\mathit{S}\mathit{J}\mathit{R}}_{\mathit{j}}$	Years of Indexing in Web of Science
1	Business Horizons	100	2	0.299	0.036	8383	2942	2174	1957–2020
2	Research Policy	28	1	0.084	0.018	4695	3663	3666	1971–2021
3	Journal of Corporate Finance	23	1	0.069	0.018	3856	2665	1894	1994–2020
4	Journal of Business Venturing	21	1	0.063	0.018	3521	4268	7107	1985–2020
5	Journal of Technology Transfer	21	2	0.063	0.036	1760	2462	1768	1977–2020
6	European Planning Studies	16	1	0.048	0.018	2683	1743	1214	1993–2020
7	Creativity and Innovation Management	15	1	0.045	0.018	2515	1422	1148	1992–2020
8	Technovation	13	1	0.039	0.018	2180	2937	2,3	1981–2020
9	Asia Pacific Business Review	11	1	0.033	0.018	1844	0.746	0.424	1994–2020
10	IEEE Transactions on Engineering Management	8	1	0.024	0.018	1341	1255	0.702	1969–2020
11	Entrepreneurship Research Journal	8	2	0.024	0.036	0.671	0.84	0.395	2015–2020
12	Strategic Entrepreneurship Journal	7	1	0.021	0.018	1174	3242	5061	2011–2020
13	Journal of Business Research	6	1	0.018	0.018	1006	2852	2049	1973–2021
14	Journal of Service Management	6	1	0.018	0.018	1006	2537	2658	2009–2020
15	International Journal of Innovation management	6	2	0.018	0.036	0.503	0.996	0.572	2008–2020
16	2018 IEEE International Conference on Engineering, Technology and Innovation (ICE/ITMC)	5	1	0.015	0.018	0.838	-	-	-
17	Learning, Media and Technology	5	1	0.015	0.018	0.838	2154	1355	2005–2020
18	Triple Helix	5	1	0.015	0.018	0.838	-	-	-
19	International Food and Agribusiness Management Review	4	1	0.012	0.018	0.671	0.901	0.474	1998–2020
20	Research-Technology Management	3	1	0.009	0.018	0.503	1587	0.811	1988–1989, 1995–2020
21	Ideas in Marketing: Finding The New and Polishing The Old	2	1	0.006	0.018	0.335	-	-	-
22	International Journal of Innovation and Learning	2	1	0.006	0.018	0.335	0.628	0.225	2003, 2005–2014, 2018, 2020
23	Optics Education and Outreach IV	2	1	0.006	0.018	0.335	0.261	0.192	1963–2020
24	Proceedings of The 8th European Conference on Innovation and Entrepreneurship, vol. 2	2	1	0.006	0.018	0.335	-	-	-
25	R & D Management	2	1	0.006	0.018	0.335	1.53	1253	1970–2020
26	Zeitschrift fur Wirtschaftsgeographie	2	1	0.006	0.018	0.335	0.772	0.596	1978–1981, 1984, 1988–2020
27	2017 IEEE 26th International Symposium on Industrial Electronics (ISIE)	1	1	0.003	0.018	0.168	-	-	-
28	Baltic Journal of Economic Studies	1	1	0.003	0.018	0.168	-	-	-
29	Basiq International Conference: New trends in sustainable business and consumption 2018	1	1	0.003	0.018	0.168	-	-	-
30	California Management Review	1	1	0.003	0.018	0.168	2355	1806	1970–2020
31	Ciriec-Espana Revista de Economia Publica Social y Cooperativa	1	1	0.003	0.018	0.168	-	-	-
32	Entrepreneurship and Regional Development	1	1	0.003	0.018	0.168	1942	1673	1989–2020
33	European Journal of Management and Business Economics	1	1	0.003	0.018	0.168	1318	0.691	2016–2020
34	International Entrepreneurship and Management Journal	1	1	0.003	0.018	0.168	2309	1338	2006–2020
35	Proceedings of The 10th European Conference on Innovation and Entrepreneurship (ECIE 2015)	1	1	0.003	0.018	0.168	-	-	-
36	Economic and Social Development (ESD)	1	2	0.003	0.036	0.084	-	-	-
37	International Journal of Engineering Pedagogy	1	2	0.003	0.036	0.084	1231	0.437	2018–2020
38	2017 IEEE European Technology and Engineering Management Summit (E-TEMS)	0	1	0.000	0.018	0.000	-	-	-
39	3rd World Multidisciplinary Civil Engineering, Architecture, Urban Planning Symposium (WMCAUS 2018)	0	1	0.000	0.018	0.000	0.484		2009–2020
40	Academic Entrepreneurship and Community Engagement: Scholarship in action and the Syracuse miracle	0	1	0.000	0.018	0.000	-	-	-
41	African Journal of Science Technology Innovation & Development	0	1	0.000	0.018	0.000	0.582	0.225	2013–2020
42	Economic and Social Development	0	1	0.000	0.018	0.000
43	Journal of Organizational Change Management	0	1	0.000	0.018	0.000	0.915	0.513	1988–2020
44	Journal of Private Equity	0	1	0.000	0.018	0.000	0.136	0.129	2007–2019
45	New Challenges of Economic and Business Development – 2019: Incentives for Sustainable Economic Growth	0	1	0.000	0.018	0.000	-	-	-
46	Proceedings of The International Conference on Engineering, Science, and Industrial Applications (ICESI 2017)	0	1	0.000	0.018	0.000	-	-	-

Source: own elaboration.

in descending order. The formulas also required information about the total size of the set, which is here $c_J^{\mathsf{\Sigma }}=334$ i $p_J^{\mathsf{\Sigma }}=56$.

Original Pattern	Applied Pattern
$i_j=\frac{c_J^{\mathsf{\Sigma }}}{p_J^{\mathsf{\Sigma }}};j\in J,J=\left\{j:j=\stackrel{-}{1,J}\right\}$	$i_j=\frac{i_j^c}{i_j^p};j\in J,J=\left\{j:j=\stackrel{-}{1,J}\right\}$	(1)
$c_J^{\mathsf{\Sigma }}={\displaystyle \sum _1^J} c_j;j\in J,J=\left\{j:j=\stackrel{-}{1,J}\right\}$	Original	(2)
$p_J^{\mathsf{\Sigma }}={\displaystyle \sum _1^J} p_j;j\in J,J=\left\{j:j=\stackrel{-}{1,J}\right\}$	Original	(3)
Only in descriptive form	$i_j^c=\frac{c_j}{c_J^{\mathsf{\Sigma }}}$	(4)
Only in descriptive form	$i_j^p=\frac{p_j}{p_J^{\mathsf{\Sigma }}}$	(5)

where:

• $J$—all analyzed sources,
• $i_j$—the impact factor of the j-th source in the researched subject area,
• $c_j$—number of citations of the j-th source in the researched subject area,
• $p_j$—number of publications in the jth source in the researched subject area,
• $c_J^{\mathsf{\Sigma }}$—the sum of citations of all J analyzed sources in the researched subject area,
• $i_j^c$—the ratio of the number of citations of the jth source to the sum of the citations of all J analyzed sources in the researched subject area,
• $p_J^{\mathsf{\Sigma }}$—sum of publications in all J analyzed sources in the researched subject area,
• $i_j^p$—the ratio of the number of publications in the jth source to the sum of publications in all J analyzed sources in the researched subject area.

The improvements made included modifying the first formula and supplementing the mathematical description of the method with additional Equations (4) and (5). Errors in the first formula most likely resulted from a mistake in the notation, because while the formula itself did not agree with the written description, the ratios calculated by the original authors seemed correct. Applying it as it is would result in obtaining the same value of $i_j$ for each source, because it was a quotient in which the dividend and divisor remained constant for the entire set. Therefore, a correction was made according to the mentioned verbal description and it was verified by carrying out several calculations on the original data.

The obtained results indicate that in the case of the study set, it is not too important whether an indicator analysis is undertaken or whether the sources are ranked straight in relation to the number of citations for each. The advantage of the source with more citations is always observed here, and at the same time the number of publications is negligible, the role of which in assessing the impact is significant only when the number of citations of two sources is equal. However, it should be strongly emphasized that this is the specificity of this collection, resulting from the relatively low popularity of the subject matter, which means that the differences in the numbers of citations and publications between records are often negligible, and the collection itself is small. In general, one would expect conclusions similar to those made in [67].

To complete the comparison, correlation coefficients were also examined, but not only between $i_j$ and the SNIP and SJR indicators recognized in the scientific community, but also between i_j and the number of citations and publications. The coefficients for the last two pairs of variables were to additionally confirm the marginal importance of the number of publications in the context of this set. Values $r\left(i_j;c_j\right)=0.9377$ and $r\left(i_j;p_j\right)=0.2269$ left no doubt—i_j is very strongly correlated with the number of citations and weakly with the number of publications.

In order to check the remaining correlations, it was necessary to first download the relevant data from the Scopus bibliographic database, which is competitive to the Web of Science, and from the SCImago Journal & Country Rank website. This was necessary because the Scopus resources are the basis of the SNIP 2020 indicators. Source Normalized Impact per Paper] and SJR 2020 [eng. SCImago Journal Rank], the latter being made available by the external research group SCImago on its website [63]. Contrary to the methodology of the original authors, the limitation related to years of indexing sources in Scopus was abandoned, assuming that the resulting problems with determining indicators are eliminated at the source of these indicators. This means that the correlation coefficients did not take into account only records where the SNIP or SJR were not provided, i.e., where they could not be calculated by the database, by definition. Obtained accordingly $r\left(i_j;SNI{P}_j\right)=0.5785$, $r\left(i_j;{SJR}_j\right)=0.4578$, which indicates an average correlation with both quantities and is in contradiction with the data described in [67]. The reason for this state of affairs may be the low popularity of the researched topic mentioned above or the high representativeness of the set in relation to its superior thematic area. The second conclusion comes from the fact that these standard indicators place a strong emphasis on the contextuality of measuring the impact of sources, which can vary greatly depending on the dynamics of citations and publications in the field under study. Therefore, the more the proposed $i_j$ index is correlated with SNIP and SJR, the greater the chance that a given set, which is a cut-off of all publications in the field, reflects this field.

It can be said that the indicator used here develops well the simple ratio of citations to publications, giving it a scale better suited to the size of the study set. Using it, researchers can generally gain—i.e., in a situation where the total number of citations exceeds the number of publications—better readability of impact figures. Nevertheless, for comparisons of sources in a general context, it is better to use classic impact indicators, such as those presented here, as well as, among others, CiteScore, Eigenfactor etc. [64]. The new i_j index may, in turn, be used locally to build a ranking of the most influential journals against the background of a given set (

Table 7. Pearson correlation result.

	${\mathit{i}}_{\mathit{j}}$	$\mathit{S}\mathit{N}\mathit{I}\mathit{P}$	$\mathit{S}\mathit{J}\mathit{R}$
$i_j$	10,000
	p = ---
$SNIP$	0.5785	10,000
	p = 0001	p = ---
$SJR$	0.4578	0.8865	10,000
	p = 0.011	p = 0.000	p = ---

Source: own elaboration.

).

Table 8. Publications with the highest number of citations.

Rank	Reference	Type	Year	Source	Keywords	Citation
1.	[15]	A	2016	Business Horizons	corporate accelerators; open innovation; corporate innovation; entrepreneurship; startups; partnerships; corporate venturing; business incubation; innovation; incubators	87
2.	[45]	A	2019	Research Policy	entrepreneurship; startups; startup programs; business incubators; evolution; management; future; model	28
3.	[12]	A	2014	Journal of Corporate Finance	startup accelerators; early-stage financing; portfolio size; information disclosure; initial public offerings; venture capital finance; entrepreneurial finance; convertible securities; empirical-evidence; up firms; intermediation; market; investment; model	23
4.	[40]	A	2019	Journal of Business Venturing	corporate accelerators; acceleration; corporate innovation; corporate entrepreneurship; corporate-startup engagement; systems perspective; grounded theory; value creation; entrepreneurship; legitimacy; innovation; model; work	21
5.	[44]	A	2019	European Planning Studies	accelerators; transnational entrepreneurs; entrepreneurial ecosystems; networks; public policy; business incubators; innovation; policy; model; firms; born	16
6.	[48]	A	2019	Journal of Technology Transfer	accelerators; seed accelerators; startup accelerators; technology commercialization; clean technology; business incubators; new venture creation; entrepreneurial orientation; business performance; moderating role; market; innovation; incubator; linking; model	16
7.	[29]	A	2018	Creativity and Innovation Management	technological threats; startups; mechanisms; success	15
8.	[41]	A	2019	Business Horizons	corporate accelerator; new venture; startup; established firm; open innovation	13
9.	[53]	A	2019	Technovation	the lean startup methodology; entrepreneurial coaching; startup accelerator; entrepreneur-coach relationship; vicarious learning; business incubation; university; peer	13
10.	[32]	A	2018	Asia Pacific Business Review	start-up accelerator; entrepreneurship education; human capital; social capital; entrepreneurial learning; entrepreneurial self-efficacy; networks; mentors; design thinking; lean start-up approach; australia; university entrepreneurship education; firm performance; business; innovation; industry; networks; growth; servitization; investments; experiences	11

Source: own elaboration.

presents the most frequently cited publications in the area of accelerators according to the Web of Science database. It includes e.g., data, year of publication and number of citations.

The next part of the ratio analysis—in relation to the publication—was again carried out using the author’s method. The focus is on the claim that comparing works only in terms of citations is not reliable, because the number of times a given work may have been cited is related to how long it has been available. This means that the most influential papers should be considered not only the most frequently cited, but also the shortest since publication. With this in mind, the so-called citation rate per year $c_p^Y$, defined by Equation (6), which will also be used in this work in a duly adapted form. Both versions, before and after the change, are shown below as Equation (6).

Original Pattern	Applied Pattern
$c_p^Y=\left|\frac{c_p}{\left(y_c-y_p-1\right)}\right|;p\in P,P=\left\{j:j=\overline{1,P}\right\}$	$c_p^Y=\frac{c_p}{\left(y_c-y_p+1\right)};p\in P,P=\left\{j:j=\overline{1,P}\right\}$	(6)

where:

• $P$ —all analyzed publications,
• $c_p^Y$—coefficient of the number of citations per year in the p-th publication,
• $c_p$—number of citations of the p-th publication,
• $y_c$—current year (Gregorian calendar),
• $y_p$—year of p-th publication (Gregorian calendar)

The original shape of the formula is correct, but it has some imperfections due to the fact that the results of its use have been limited to only the 20 most influential publications [1]. If such a restriction were not applied, it might turn out that when $y_p=y_c-1$, to $c_p^Y=\left|\frac{c_p}{0}\right|$, which is an expression that makes no numerical sense. Such a situation did not occur in the quoted paper, because in the limited set of publications, each of them met the inequality $y_p<y_c-1$. Therefore, it was decided here to change the formula and thus simplify the expression without violating its important property, which allowed determining the impact also for works published in the same year in which the coefficient was calculated. The formula in the new variant assigned a weight of 1 to citations of publications from the current year, 0.5 from a year ago, 0.33 from two years ago, 0.25 from three years ago, etc., which is shown together with the data used for the calculations in

Table 9. List of all publications.

P	References	Source	cp	yp	${\mathit{c}}_{\mathit{p}}^{\mathit{Y}}(+1)$	${\mathit{c}}_{\mathit{p}}^{\mathit{Y}}(-1)$	Rank	References	Source	cp	yp	${\mathit{c}}_{\mathit{p}}^{\mathit{Y}}(+1)$	${\mathit{c}}_{\mathit{p}}^{\mathit{Y}}(-1)$
1	[15]	Business Horizons	87	2016	14.5	21.75	29	[58]	Regional Development	1	2021	1	1
2	[45]	Research Policy	28	2019	9333	28	30	[62]	International Management Journal	1	2021	1	1
3	[12]	Journal of Corporate Finance	23	2014	2875	3833	31	[57]	European Journal of Management and Business Economics	1	2020	0.5
4	[40]	Journal of Business Venturing	21	2019	7	21	32	[60]	California Management Review	1	2020	0.5
5	[44]	European Planning Studies	16	2019	5333	16	33	[51]	International Journal of Engineering Pedagogy	1	2019	0.333	1
6	[49]	Journal of Technology Transfer	16	2019	5333	16	34	[30]	New Trends in Sustainable Business	1	2018	0.25	0.5
7	[29]	Creativity and Innovation Management	15	2018	3.75	7.5	35	[31]	Baltic Journal of Economic Studies	1	2018	0.25	0.5
8	[41]	Business Horizons	13	2019	4333	13	36	[37]	CIRIEC-Espana Revista de Economia Publica Social y Cooperativa	1	2018	0.25	0.5
9	[53]	Technovation	13	2019	4333	13	37	[20]	2017 IEEE 26th International Symposium on Industrial Electronics	1	2017	0.2	0333
10	[32]	Asia Pacific Business Review	11	2018	2.75	5.5	38	[17]	Economic And Social Development	1	2016	0.167	0.25
11	[36]	Entrepreneurship Research Journal	8	2018	2	4	39	[14]	ECIE 2015	1	2015	0.143	0.2
12	[38]	IEEE Transactions on Engineering Management	8	2018	2	4	40	[1]	International Journal of Innovation Management	0	2021	0	0
13	[47]	Strategic Entrepreneurship Journal	7	2020	3.5		41	[64]	African Journal of Science Technology Innovation & Development	0	2021	0	0
14	[46]	Journal of Business Research	6	2019	2	6	42	[59]	Entrepreneurship Research Journal	0	2020	0	0
15	[19]	International Journal of Innovation Management	6	2017	1.2	2	43	[56]	Raumforschung und Raumordnung	0	2020	0	0
16	[22]	Journal of Service Management	6	2017	1.2	2	44	[55]	Journal of Organizational Change Management	0	2020	0	0
17	[3]	Journal of Technology Transfer	5	2021	5	5	45	[43]	Journal of Private Equity	0	2019	0	0
18	[63]	Learning Media and Technology	5	2021	5	5	46	[54]	WMCAUS	0	2019	0	0
19	[35]	Triple Helix	5	2018	1.25	2.5	47	[52]	International Journal of Engineering Pedagogy	0	2019	0	0
20	[28]	2018 IEEE ICE/ITMC	5	2018	1.25	2.5	48	[2]	New Challenges of Economic and Business Development	0	2019	0	0
21	[26]	International Food and Agribusiness Management Review	4	2018	1	2	49	[27]	Technology Entrepreneurship	0	2018	0	0
22	[25]	Research-Technology Management	3	2018	0.75	1.5	50	[34]	Revista GEINTEC-Gestao Inovacao e Tecnologias	0	2018	0	0
23	[16]	Optics Education and Outreach IV	2	2016	0.333	0.5	51	[33]	Revista Eletronica De Estrategia E Negocios—REEN	0	2018	0	0
24	[42]	International Journal of Innovation and Learning	2	2019	0.667	2	52	[21]	2017 IEEE European Technology And Engineering Management Summit	0	2017	0	0
25	[49]	Zeitschrift für Wirtschaftsgeographie	2	2019	0.667	2	53	[18]	ICESI 2017	0	2017	0	0
26	[39]	R & D Management	2	2019	0.667	2	54	[23]	Economic and Social Development	0	2017	0	0
27	[13]	Ideas in Marketing	2	2015	0.286	0.4	55	[24]	Economic And Social Development (ESD)	0	2017	0	0
28	[11]	8th European Conference on Innovation	2	2013	0.222	0.286	56	[10]	Academic Entrepreneurship	0	2011	0	0

Source: own elaboration.

, whose records are ranked in descending order of the coefficient $c_p^Y$.

At this point, we have to agree with the original authors—the most influential works are not necessarily the best in terms of the number of citations they received. This phenomenon can be observed very clearly at the beginning of Table 9, where there are 2 publications (with the same number of citations and the same year of publication) [3,57] occupying only the 17th place in the ranking according to the number of citations, but the number of these citations was obtained in such a short time that they were ranked 6th in terms of potential impact. It should be noted, of course, that at least in the case of the first publication, this discrepancy is largely conditioned by the common tendency to cite review papers more often.

6. Conclusions

This publication is the answer to the research question: What is the current state of knowledge in the field of start-up accelerators? In order to answer this question, the tools of two research methodologies were used. The first stage involved a systematic review of the literature found in the Web of Science database. For this purpose, special criteria for the analysis of titles, abstract content and keyword range were used. This made it possible to complete a set of 60 publications, which were subjected to a detailed analysis in terms of content. The result was the selection of a set of 56 publications that made up the final research sample and are described in the third chapter. The collected items were then subjected to detailed research, which was presented during the bibliometric analysis (the second research methodology). This stage of the work allowed to present the dynamics of changes in the number of studies on start-up accelerators published in the period 2011–2021. The results of research on the impact of geographical aspects in the context of research in this area of science are also presented. This analysis referred to the presentation of the productivity of researchers from specific continents and countries. The further part of the work presents the productivity of individual authors, sources publishing the analyzed studies and research units that participated in the work on start-up accelerators. By specifying the thematically analyzed publications, the distribution of the topics undertaken in terms of the described types of accelerators and the motivation to conduct research was also presented. This made it possible to highlight issues whose clarification was the aim of the work of many scientists in recent years. This publication presents the current state of knowledge, detailing the thematic work and outlining the context limiting specific research. An extensive literature review and bibliometric analysis of the collected publications allowed to organize the previous research in one place. Thus, the study is a valuable material both for theoreticians who want to conduct further research in this area of science, and for representatives of the practice, which includes the management staff of corporations, independent accelerators, start-ups, or government agencies that often finance the activities of accelerators.

Research proves that the topic of start-up accelerators is being intensively developed, and scientists are constantly looking for new directions that will deepen the available knowledge in this area of science. The need for research results from the significant impact of this form of innovation support on the current entrepreneurship, where innovation often determines the competitive ability of enterprises, and society is constantly looking for new solutions to improve its standard of living. Although start-up accelerators are a relatively new facility in the entrepreneurial ecosystem, they already have a large impact on its functioning. This paper presents the current approaches defining research on start-up accelerators. Based on the analysis of the analyzed period, there is a clear difference in the level of interest in the topic of start-up accelerators over time. The first identified study was published in 2011 and was the only material on the subject published that year. In the following years, this area of research did not gain wide interest in the scientific community, which resulted in only 2 publications in the period 2012–2014. The year 2015 should be considered the beginning of the growing trend of interest in start-up accelerators. The real peak of interest for the period discussed here was in 2018–2019, when a total of 29 (14 and 15 publications, respectively) studies in the area of science we studied were published. In 2020, we can observe a decrease in interest in the subject of start-up accelerators, which results in the appearance of only 6 publications. This is probably related to the COVID-19 pandemic and its impact on scientific activity, visible in the change of research priorities and communication difficulties.

In the geographical context, we can see that the largest number of publications is related to the activities of researchers from Europe (participation in the work on 49 publications, which were cited 195 times) and North America (participation on the work on 15 publications, which were cited 217 times). Specifically, the results of scientists from North America were worked only by researchers from the United States, and the achievements of Europe—scientists from 17 different countries. The most distinguished in this aspect include the works of scientists from: Germany (participation in the work on 8 publications, which were cited 43 times), Norway (participation in the work on 2 publications, which were cited 23 times), France (participation in the work on 3 publications, which were cited 23 times) cited 21 times) and Scotland (participation in the work on 2 publications, which were cited 21 times). It is also worth emphasizing the achievements of scientists from Australia (participation in the work on 3 publications, which were cited 32 times) and India (participation in the work on 1 publication, which was cited 21 times). Already on this basis, we can see that the location of research on the topic of start-up accelerators is strongly related to the level of wealth and economic development of a given region.

The vast majority of works are collective in nature. We identified 131 authors while compiling 56 publications. The research did not show dominant individuals, the authors with the largest number of publications prepared 3 papers on the researched subject each. The author with the highest number of citations is T. Kohler, whose one classified paper was cited 87 times. The total number of citations of all collected publications was 334, and the number of sources responsible for published studies was 50. The source with the highest ratio of the number of citations to the number of published publications is the scientific journal “Business Horizons”—2 papers were published in it, which were cited 100 times. 96 research units participated in the creation of 56 indexed publications. In about 1/3 of them (27) we can distinguish the participation of only one research unit. Other works were developed in cooperation with representatives of several research units. The centers associated with the largest number of publications are: Massachusetts Institute of Technology (MIT), Edith Cowan University, University of Valencia and Comenius University Bratislava. The units whose publications have achieved the largest number of citations are: Hawaii Pacific University, University of California (Berkeley) and the University of Innsbruck—each of them received 87 citations, and additionally all these units are associated with the most frequently cited paper from the set of analyzed publications. The analysis of the literature allows to determine the current directions of research. So far, most publications (18) dealt with the general subject of accelerators, but an equally significant part of the research was dedicated to corporate accelerators (15 publications). The analysis of the functioning of seed and academic accelerators (7 publications each) aroused significant interest. Other studies focused on other types and forms of accelerators or presented several types in detail. In terms of specific motivations that dominated research on the subject of start-up accelerators, we can distinguish attempts to systematize them and bring closer the issue of their diversity (15 publications) and work on understanding the essence of cooperation between accelerators and start-ups (13 publications). In addition, the works often presented reports on acceleration programs (11 publications) and defined the scope of designing, implementing and running start-ups and accelerators (11 publications).

The research sample of 56 publications is not very numerous, however, the relatively young age of the researched issue should be taken into account here. In fact, the years 2011–2015 can be considered as the beginning of research in this thematic area. Despite such a large collection, the authors of the work decided that the research gap related to the lack of systematization of the current achievements in this field of science required supplementing, and the presented study fulfills this role. Future works of the authors will focus on deepening the knowledge on the functioning of startup accelerators and assessing the effectiveness of their operation, with particular emphasis on the changed conditions of their operation resulting from the post-covid stage in the economy.

The following points are crucial for the authors of this publication:

• This publication answers the research question regarding the current state of knowledge on start-up accelerators, using two research methods: systematic literature review and bibliometric analysis.
• Research shows that the topic of start-up accelerators is being intensively developed, and scientists are looking for new directions that will help deepen knowledge on this subject. Start-up accelerators are a relatively new object in the entrepreneurial ecosystem, but they already have a large impact on the functioning of enterprises and society, which is constantly looking for innovative solutions. The publication presents current approaches defining research on start-up accelerators and differences in interest in this topic in different years. After the initial lack of interest, a growing trend began in 2015, and 2018–2019 saw a real peak in the number of publications. In 2020, interest in the topic declined, possibly due to the COVID-19 pandemic.
• The location of research on start-up accelerators is strongly related to the level of wealth and economic development of a given region, with most publications coming from Europe and North America.
• Most of the publications are collective in nature, no dominant individuals have been identified, and most of the papers were created in cooperation with representatives of several scientific units.
• So far, most of the publications concerned the general subject of accelerators, but an equally important part of the research was devoted to corporate accelerators and the analysis of the functioning of seed and academic accelerators. Future work will focus on deepening the knowledge on the functioning of startup accelerators and assessing the effectiveness of their operation, with particular emphasis on the changed conditions resulting from the COVID-19 pandemic.

To sum up, the described publication presents the current state of knowledge in the field of start-up accelerators and illustrates the growing interest in this area of science in recent years. Research on start-up accelerators is important due to their significant impact on modern entrepreneurship and the search for new solutions to improve the standard of living. The publication is valuable material for both theoreticians and practitioners who want to broaden their knowledge on this subject.