Territorial Context and Spatial Interactions: A Case Study on the Erasmus K1 Mobility Datasets

Abstract

This study evaluates the impact of different territorial contexts on academic mobility within the framework of the Erasmus Programme, using data on Key Action 1 exchanges between 2015 and 2023. Using official EU datasets and a gravity model framework, the research investigates how economic performance, geographical distance, EU membership, AUF (Agence Universitaire de la Francophonie) regional affiliation, and state contiguity shape international academic flows. The research developed two gravity models: one aimed to measure the potential barriers to academic flows through a residuals analysis, and the second integrated territorial delineations as predictors. In both models, the core of the explanatory variable is formed by indicators describing the economic performance of states and the distance between countries. When applied, the models converge in emphasizing that the inclusion of states in different territorial configurations has a strong effect on the structuring of academic flows. This suggests that the Erasmus Programme exhibits trends of overconcentration of flows in a limited number of countries, questioning the need for a more polycentric strategy and a reshaping of the funding mechanisms. Even if the gravity models behave well, given the limited number of predictors, further studies may need to incorporate qualitative indicators for a more comprehensive evaluation of the interactions.

1. Introduction

Since the inception of the Erasmus Programme, it has quickly become clear that it would be transformed into one of the EU’s “showroom” initiatives due to its extensive policy implications [1,2]. At the core of the Programme lies the concept of academic mobility of students and teaching staff, a mobility that is perceived as one of the key factors of EU internationalization. In 2023, the number of participants in mobility activities reached 15.1 million [3], covering virtually 160 countries [4] that were eligible for various actions within the programme’s framework. The chronological extent of the project (38 years) is already sufficiently long to consider it a mature EU project, similar to other policy instruments such as territorial cohesion or agricultural schemes. The most recent phases of evolution of the Erasmus Programme are highly linked to major policy objectives like digital transition, inclusion and diversity, and environmental and climate change, shaping its new frameworks of action and new priorities, especially in the K1 (Key Action 1) grants. The ERASMUS programme (EuRopean Action Scheme for the Mobility of University Students) was officially launched in 1987 with the aim of facilitating student mobility within 11 of the 12 member states of the European Economic Community (Belgium, Denmark, France, West Germany, Greece, Ireland, Italy, the Netherlands, Portugal, Spain, and the United Kingdom). Following the establishment of the European Higher Education Area (EHEA) in 2010, the programme was expanded and, since 2014, under the name ERASMUS+, it has become a key component of the EHEA. Following Switzerland’s partial withdrawal (2014) and the European Union’s enlargement policy, the programme currently operates in 37 countries, namely the 27 members of the EU and 10 other countries called “third countries not associated with the programme” (Albania, Bosnia and Herzegovina, Liechtenstein, Iceland, Kosovo, North Macedonia, Montenegro, Norway, Serbia, and Türkiye). The United Kingdom’s return to the programme is currently being negotiated. With some exceptions, all other countries in the world can benefit, under various conditions, from certain actions of the program. For the period 2021–2027, the programme has accredited 6 117 higher education institutions. Of these, 76% (4 648) are concentrated in just five countries: Spain (30.6%), France (28.5%), Germany (6.2%), Italy (5.7%), and Poland (4.95%). Although the current funding for the programme includes, in addition to Jean Monnet activities, two new key actions (Supports cooperation among organizations and institutions and Supports policy development and cooperation), most of the budget (59% between 2021 and 2023) is directed toward the original idea, namely “Supports learning mobility of individual projects”. Between 1987 and 2024, over 16 million students and teachers benefited from this funding axis, contributing to the construction of a pan-European scientific and educational space and deepening the sense of community belonging. Between 2014 and 2024, the ERASMUS+ Programme funded 9 590 601 learning mobility, of which 4 199 249 (43.8%) were specific to higher education [5,6]

1.1. Highlights of the Scientific Literature on the Erasmus Programme

Given its significant importance as a success story for EU decision-makers, the study of the Programme received considerable attention. The literature on the Erasmus Programme and its implications is extensive and has been developed across various fields, largely due to the longevity of this successful EU programme. Research addressing Erasmus spatial flows within precise territorial frameworks, based on quantifiable criteria, is limited, mainly due to the lack of reliable data. Therefore, identifying sound criteria for analyzing the configuration of flows was a challenge and required examining the key drivers. The spatial interactions of Erasmus students and academic staff are shaped by the facilities provided by the European Union and its partners. However, the orientation and intensity of these flows result from numerous influencing factors, which can be integrated into the pull-push model [7,8,9]. Among the pull factors, the literature highlights academic excellence, with a strong role for countries hosting top universities [10], career prospects after graduation, driven by the prestige of the obtained degree and the size of the labour market [11], a cosmopolitan university environment and a rich cultural life, institutional support through the number of Erasmus agreements, the diversity and attractiveness of programmes, and the quality of the selection process in host universities [12]. Most of these correlate with a high GDP per capita of both states’ partners. Equally influential are the push factors, such as the precarious economic situation in some countries, which remain primarily senders; the poor quality of education and research, which pushes talented youth into the brain drain flow [13,14]; and psychological factors, such as the demonstration effect or the desire to experience contexts different from those in the country of origin. The literature also notes that, globally, transnational networks of academic mobility are stable over time, that hemophilia among countries determines patterns of student exchanges, and that the most relevant connections exist between neighbouring countries [15]. The presence of a core–periphery configuration in the European student mobility network is further emphasized, with economic benefits and investments in education being key elements for university attractiveness. In line with developments specific to the French school of social analysis [16,17,18], it is worth noting the territorial inequalities in access to Erasmus grants, which tend to reproduce the hierarchy of prestige inequalities among European countries and universities. Other research brings complementary perspectives into the debate, such as the concept of the mobility capsule, proposed for the cross-border circulation of university staff mobility within European consortia, the routine of uprooting, and cosmopolitan social closure [19]. Similarly, the research highlights and substantiates the concept of “hotspot” destinations in certain European regions, which emerge as a result of successful regional policies that stimulate internationalization [20]. Directly or indirectly, several studies reveal the role of linguistic affinities and mutual openness in establishing inter-institutional agreements and facilitating Erasmus mobility [15,21]. The influence of ethno-cultural minorities in many European states is also noted. These tend to generate Erasmus flows toward universities in regions with similar cultural characteristics and a shared history [22,23], but the phenomenon is often diluted in the large mass of university mobility. Even the natural factors may play a certain role, such as the “holiday climate” or the spectacular landscapes of some countries. However, in larger states, natural conditions may differ from one region to another, and the climatic factor assumes diverse geographical connotations. Therefore, in a country-level analysis, this factor tends to be irrelevant. Studies instead consider the impact of international student mobility in the context of climate change [24]. Most of the factors mentioned are subjective and difficult to quantify based on rigorous criteria for inclusion in spatial gravity models, also because reliable global data is lacking. As a result, by inventorying the available open-source databases and the findings of other research [25,26,27], we opted for a multi-scale analysis, integrating both global and macro-regional patterns of Erasmus interactions.

In geography and the social sciences, research primarily focuses on understanding how academic mobility is integrated into processes of territorial networking and beyond, as well as the internationalization and globalization of knowledge [28,29]. The studies can be broadly divided into three categories: the analysis of the Erasmus networks from a geostatistical perspective [30], with a focus on network configuration [31]; the identification of mobility patterns using gravity models [32,33,34]; the evaluation of factors interfering with the spatial interactions derived from the Erasmus flows [35]. Although widely used in the analysis of various types of international flows, the gravity model is also a method used in specialized studies on mobility patterns [36,37], including academic mobility [38,39]. In the case of academic mobility, the model uses the common logic of international flows whose intensity depends on their attractiveness and existing barriers or costs. The application of the gravity model in studying academic mobility facilitated by the Erasmus programme is justified by the need to understand the main push and pull factors that shape the direction of academic flows. In this sense, the literature confirms the application of the gravity model in the analysis of academic mobility, highlighting the relevance of economic and demographic factors, as well as linguistic similarities and students’ preference for universities with English-language study programmes [40,41,42], factors that shape the direction of academic flows. The studies implemented at the NUTS 3 scale [43] emphasized the role played by the predictors’ datasets in explaining mobility, which are also difficult to extract for countries with different statistical traditions, outside the EU. The estimation of barrier effects on spatial interactions has a solid theoretical foundation, rooted in the development of gravity models in population geography [44], spatial analysis [45,46], regional science, and the economics of trade [47,48,49]. Our approach estimates this effect using different regional delineations of the Erasmus network of cooperation at the national level. The first two territorial contexts we investigate—namely, EU membership and the barriers imposed by state borders—are systematically used in understanding spatial interactions [50,51,52]. Therefore, the use of the gravity model in the present research is an application of a previously tested and validated methodological framework for understanding international flows of various types.

1.2. Objectives of the Exploratory Analysis

The primary objective of this study is to gain an in-depth understanding of the recent dynamics of the Erasmus mobility network and to elucidate how different territorial contexts influence the orientation and intensity of student and teaching staff flows at the country level within a global context. The leading hypothesis of the study posits that, besides the state’s economic performance and distance, the territorial contexts (e.g., EU belonging, or participation in university alliances) determine how the academic interactions are shaped, by introducing selective filters on the flows. In certain circumstances, these filters act as barriers, the effectiveness of which is evaluated by the methodology we implement. In other cases, the impact is more subtle, and the territorial belonging to major economic and political macro-regions is essential in explaining the excess of interactions.

Subordinate to this main hypothesis, two secondary hypotheses are derived, which guide the research. The first one states that different territorial contexts (political, cultural affiliations, etc.) have a direct impact on the configuration of the gravity models used to describe Erasmus academic exchanges. The second one considers that the contiguity between states stimulates the intensity of flows, which can explain the positive deviations from the standard spatial interaction models.

The exploration and validation of this set of hypotheses involved the development of objectives guiding our work, namely:

• Construction of a baseline gravity model relying on a limited set of predictors (countries’ economic performance at origin and destination and distance between states).
• A progressive introduction of different territorial and spatial contexts, as predictors, in the gravity model.
• Identification of the barrier effects on the Erasmus academic exchanges by evaluating the different coefficients obtained during the implementation of specific quantitative models.
• Mapping the results, mainly the deviations from the theoretical frame. These deviations are a proxy for the deficit or surplus of attractiveness that different countries will deploy in the network of Erasmus interactions.

2. Materials and Methods

Our research investigates the role played by different territorial contexts of academic mobility, with a focus on the effect of barriers that create different forms of impedance in the network of Erasmus exchanges. The scale of analysis is country level, as the research also includes states associated with the Programme that do not belong to the EU and for which a comparative and harmonized sub-national geometry is not possible to build. Given the complexity of academic mobility flows, we added two supplementary territorial frames—the inclusion of states in two AUF (Agence Universitaire de la Francophonie) regions—Eastern and Central Europe (DRECO—Direction Régionale de l’Europe Centrale et Orientale) and Western Europe (DREO—Direction Régionale de l’Europe Occidentale), in line with the agency’s official delineation available at the following address https://www.auf.org/les_membres/nos-membres/ (accessed on 28 September 2025). The introduction to the analysis of these two regional frames is justified by the fact that the university alliances, by their size, complexity, and institutional organization, are able to significantly structure and channel academic exchanges.

2.1. Inventory of Data Input for Gravity Models

The analysis of the Erasmus system of academic mobility is based on the downloadable statistics and metrics provided by the EU Commission as open data [53]. The datasets are available for a chronological period spanning 2015–2023, with a relatively harmonized structure of indicators. Our investigation used only three distinct statistical collections for 2015, 2019, and 2023, aiming to provide a comparative frame for the analysis, with a four-year gap. The primary reason for this option was the clear distortion in the data caused by the pandemic period (2020–2022). During this period, some interactions were cancelled or switched to online teaching, making the data unusable for investigation. The three statistical sources retained were filtered, and only the indicators describing academic mobility (student mobility for studies and staff mobility for teaching) were integrated into our spatial database, excluding other forms of international cooperation or auxiliary flows like training missions, practice, or job shadowing. This restriction was necessary in order to focus only on the academic dimension of the Erasmus Programme. The raw data is organized as an origin-to-destination flows matrix, linking partner universities. Additional data concerning the field of study, the participant’s gender, and the number and duration of the mobility are also present in the statistical sources. The number of origin-destination links selected for the analysis varies in time (239,251 in 2015, 283,343 in 2019, and 279,705 in 2023). Geocoding the dataset is a technical challenge [25] because there are three different options that will open separate avenues of research. One can implement a geocoding technique based on universities as geographical objects and flow sources. A second possibility is to aggregate the flows by sub-national administrative geometries (e.g., NUTS3 and equivalent in non-Eurostat covered states). Finally, a synthetic aggregation at the country level can also be created. Our research identified an option for the last method of data summarization, with the main reasons being its increased potential to explore the consolidated flows using gravity models and geostatistical tools. The other options for aggregation were also taken into account, but the lack of auxiliary indicators (e.g., harmonized and sound economic performance at the subnational administrative scale) precluded further study of the academic mobility system.

Once the chronological datasets describing the inter-state Erasmus flows were created, the predicting variables of the gravity models are integrated into each mobility matrix. These indicators describe the economic performance of countries at three points in time (2014, 2018, and 2022) and the territorial context that influences these interactions. In our model, the economic performance of countries is approximated by GDP per inhabitant, an indicator commonly used in the literature/other studies [54], despite the inherent criticism. The source of the harmonized GDP data is the Our World in Data platform, the values being compiled from multiple sources (mainly the World Bank). The choice to use data from the previous year (e.g., 2014 instead of 2015) was based on the assumption that both students and staff would arbitrate the utility of mobility using known information about their financial status, rather than future projected information [55]. The unit of measure is the International USD at 2021 prices.

The territorial and spatial contexts integrated in our spatial database take multiple forms. They can be declined on 3 levels. The first one concerns the countries’ integration in macro-economic and political regions—the EU. We assume that, ceteris paribus, states belonging to the EU will generate superior flows, compared to two states in other geopolitical situations. This assumption is at the core of the gravity models methodology applied to trade interactions or foreign direct investments. The second level of territorial context is created by the countries’ integration into large international academic structures like the AUF. Although the database we used has a global extent, the strong concentration of Erasmus flows in Europe allowed us to use only two AUF regions—DRECO and DREO. Our hypothesis suggests that being a member of these regions will impact the volume of flows, especially for the francophone component of studies. Finally, the spatial context is described by the countries’ contiguity. We considered that neighbour states will present a higher probability of developing academic mobility, compared to separated ones. Despite being a simple indicator, it will pose some problems of interpretation and validation in the case of countries with geographical specificities (islands). In our models, we altered the situation of the United Kingdom and Denmark, considering that they are contiguous to France and Sweden. Moreover, using a binary indicator of countries’ adjacency overlooks some political realities that are at work in the EU, the Schengen space. With few punctual exceptions, crossing a Schengen border is easier than in other situations, making the indicator rather continuous than categorical, in terms of values.

If the indicators used to describe the factors that leverage the flows strongly exhibit stationarity over time, the flows are subject to changes, not only in volume, but also in existence. Between 2019 and 2023, 1200 mobility links were disestablished, illustrated in Figure 1. The large majority were connections involving a non-EU country as a partner (1192). The dissolution of these interactions is difficult to explain, opening up many avenues for scientific speculation (including the impact of the COVID pandemic [56], geopolitical changes, Erasmus Programme’s local restructuring, etc.). For the same time interval, 492 new connections were established, following an identical pattern (an EU and a non-EU country involved). The constant reshaping of the Erasmus network poses a methodological challenge, as it can interfere with the implementation of comparative analysis, for example.

2.2. Formalization of Gravity Models Used in the Analysis of Erasmus Interactions

Once the spatial database was completed, the workflow continued with the identification of the methodological options that can provide insight into the effect of barriers affecting the Erasmus mobility. Two separate gravity models were built in order to detect these impediments on the spatial interaction. The first one (GM1—gravity model no. 1) is assumed to be the baseline one, and it is expressed in its canonical formalization as follows:

logFij = log(β₀) + β₁ × log(GDPt_O) + β₂ × log(GDPt_D) − α × log(DIST_ODt),

where

• log(β₀) = intercept of the regression model
• GDPtO = GDP/inhab. for the outgoing spatial unit (country)
• GDPtD = GDP/inhab. for the incoming spatial unit (country)
• DIST_ODt = distance between countries’ centroids

The model’s parameters (β, α) will control the impact of each predictor on the deployment of flows, and it will describe the morphology of the statistical association between the flows and factors such as economic performance and the spatial separation between countries [57,58].

The second model (GM2–gravity model no. 2) adds a binary predictor that takes into account the role played by the political, economic, and academic territorial context of each pair of states analyzed:

logF_ij = log(β₀) + β₁ × log(GDP_t_O) + β₂ × log(GDP_t_D) +β₃ × TC − α × log(DIST_OD_t),

where

TC = countries’ belonging to the EU, DRECO, DREO, or a measure of territorial contiguity between countries. Four separate binary indicators were introduced in the modelling process, allowing us to extract an evaluation of the effect of barrier (EB) for each territorial context. The values of β₃ are relevant by their intensity and sign. If the coefficient is negative, one will expect a reduction in flows compared to a standard situation. For example, if β₃ = −0.3, one will consider that the territorial effect negatively impacts the spatial interactions by 50%, all other things being equal. The evaluation is based on the following formalization [59,60]:

EB = (log base ^β3 − 1) × 100, for β₃ > 0,

EB = (1 − log base ^β3) × 100, for β₃ < 0,

where

• EB = barrier effect induced by the countries’ integration in different political, economic, or academic territorial delineations (e.g., EU, DRECO, DREO). It also incorporates the effect of states’ contiguity.
• log base = the base of the logarithmic transformation of the indicators (10, in our case).

Each model described in this methodological section provides a different, yet convergent evaluation of the role played by the country’s integration into different organizations. The first model (GM1) will be instrumentalized through residual analysis. We expect the residuals of the multiple regression equation to follow different configurations, depending on the territorial contexts we measured. For example, using DRECO integration as a theoretical illustration, we observe that the sum of residuals for countries belonging to DRECO is negative for all 3 years analyzed, indicating that the interactions in this AUF region are clearly under their potential, given their GDP and the evaluations of proximity. The second model (GM2) aims to identify specific coefficients for the effects of the barrier. These coefficients are not stationary in time, indicating how the systems of spatial interaction in the Erasmus Programme react to different political, economic, and academic stimuli. The output of the models’ implementations is described in the next section of this paper.

3. Results

The analysis of Erasmus mobility between 2015 and 2023 involved the elaboration of different gravity models for each dataset. The quality of these models varies with time. The first set of models (GM1) starts with a modest R² of 0.263 in 2015. It continues with a higher coefficient of determination in 2019, increasing to 0.393. In 2023, the quality of the model fitting was similar to that of the previous year we analyzed, remaining stable at around 0.394. Even if the magnitude of the R² coefficients is rather moderate to low and a large quantity of the flows’ variance is left unexplained, we consider that the regression models still intercept well the main explanations of the spatial interactions between countries participating in the Erasmus Programme. The limited number of predictors and the nature of the flows, which are subject to multiple cultural and socio-economic contexts, might also impact the quality of the adjustment. The VIF (variance inflation factor) tests for multicollinearity are close to 1 (a maximum of 1.111 for the GDP/inhab. describing the destination countries, in 2023). Consequently, we assume that the multicollinearity of indicators in the GM1 models is negligible.

3.1. Main Outputs of the Spatial Interaction Models

The coefficients of the multiple regressions implemented during the workflow behave as expected. The distance decay is negative and exhibits a clear reduction from 2015 to 2023. The loss of intensity of this predictor of flows can be associated with the diffusion of low-cost airlines on a global scale, thus increasing the affordability of trips, especially in the case of students. The economic performance of partner countries has a visible impact on the Erasmus mobility. The values of the coefficient are systematically higher for the GDP/inhab. associated with the destinations. The imbalance between β₁ and β₂ is somehow counterintuitive, given the budget limitations of the Erasmus grants. If the impedance of distance diminishes over the time period considered, the role of economic performance registers fluctuations (

Table 1. Model parameters of the gravity model no. 1 (GM1). No barriers were taken into account.

	Model Parameters	Value	Standard Error	t	p
Dataset for 2015	Intercept (β0)	−2.511	0.885	−2.838	0.005
	GDP2014_O (β1)	0.768	0.120	6.409	<0.0001
	GDP2014_D (β2)	0.874	0.130	6.701	<0.0001
	DIST_OD (α)	−1.097	0.067	−16.456	<0.0001
Dataset for 2019	Intercept (β0)	−0.872	0.273	−3.192	0.001
	GDP2018_O (β1)	0.447	0.032	14.091	<0.0001
	GDP2018_D (β2)	0.674	0.033	20.147	<0.0001
	DIST_OD (α)	−0.899	0.025	−35.547	<0.0001
Dataset for 2023	Intercept (β0)	−2.152	0.330	−6.521	<0.0001
	GDP2022_O (β1)	0.594	0.037	15.932	<0.0001
	GDP2022_D (β2)	0.763	0.041	18.448	<0.0001
	DIST_OD (α)	−0.868	0.031	−28.431	<0.0001

). From 2015 to 2019, both the GDP/inhab. at the origin and at the destination lose some of their explanatory power. For the next set of chronological milestones (2019–2023), the trend shifts. According to the World Bank data, the values of the GDP/inhab. indicators in 2015 were the lowest from the recent economic history of the EU—a response of the markets to the multiplication and overlaying of multiple structural and national crises. From 2015 to 2023, the indicators’ values show a constant growth, interrupted, at the EU scale, by two moments: 2020 and 2022. In many regards, EU economic trends can be extrapolated at the national scale, potentially explaining the fluctuations of the GM1 coefficients.

3.2. Analysis of the Models’ Residuals and Coefficients—The Key Role Played by the Territorial Context

Each model described above provided a set of residuals, characterized by their intensity and capacity to highlight the impact of the territorial context on the interactions between the Erasmus countries, for each year. Based on a chi-square (χ²), for all three years applied to the research datasets, the residuals follow a normal distribution, with p-values < 0.01 and 0 sums. The test of residuals normality corroborates with other descriptors of the GM 1 regression models, suggesting that they are robust. The synthetic output of the methodological approach is available in

Table 2. Effect of the barrier—a residual analysis based on the gravity model no. 1 (GM1).

		2015		2019		2023
	Intra 1	Sum of Residuals	Count of Residuals	Sum of Residuals	Count of Residuals	Sum of Residuals	Count of Residuals
DRECO	1	−23.61	124	−23.44	321	−50.84	289
	0	23.61	994	23.44	3122	50.84	2446
	Σ	0.00	1118	0.00	3443	0.00	2735
DREO	1	24.96	68	49.24	71	44.35	72
	0	−24.96	1050	−49.24	3372	−44.35	2663
	Σ	0.00	1118	0.00	3443	0.00	2735
Contiguity between states	1	−17.74	103	19.12	140	23.79	130
	0	17.74	1015	−19.12	3303	−23.79	2605
	Σ	0.00	1118	0.00	3443	0	2735
Non-EU flows	0	−10.64	32	−37.14	275	−73.09	166
EU as origin or destination	1	−84.74	416	−143.73	2487	−300.50	1889
Intra-EU flows	2	95.38	670	180.87	681	373.60	680
	Σ	0.00	1118	0.00	3443	0	2735

¹ Intra translates the different situations in which a country can be analyzed. For example, if a state is a DRECO or DREO member, it will receive a value of 1 in the database; else, it will receive a value of 0. The same applies to two countries being neighbours or not. For the EU, three situations are possible: being a member or not, and the situation of Erasmus exchanges, where only one of the states is an EU member, while the partner is not (labelled as 2).

.

The AUF regions integrated in the study are characterized by a complete opposition in terms of the sum of residuals. The Erasmus exchanges between countries that are DRECO members are generally associated with negative residuals, a situation that indicates flows under the potential if one takes into account the available GDP/inhab. at origins and destinations, or the relatively close distance between the states. From 2015 to 2023, the residuals sum doubles their value, showing that the academic interactions are severely penalized in this region. One can speculate about the factors that shaped this statistical reality and take into consideration explanations such as linguistic over-variety of DRECO states, a systemic lack of attractiveness due to the geographical imaginary of students and staff, or economic barriers. The interpretation of the sum of the residuals demands some precautions. The fact that the sign of the sum is negative will not necessarily involve the absence of positive residuals for the intra-DRECO academic mobility. For example, in 2.23, the most important inter-country relations that were underestimated by the GM 1 (standardized residuals > 1.96) are organized by a limited number of states—Poland, Türkiye, Romania, and Hungary. The strong over-estimation, in the same year, is concentrated at the scale of countries from the former Yugoslavia.

DREO is in a completely opposite situation. The sum of residuals is positive for the intra-DREO academic mobility, showing that the countries composing this AUF region deploy interactions over their potential, in terms of GDP and distance. Highly heterogeneous in terms of economic, demographic, and academic size, it is not surprising that the strongest positive residuals (>1.96) are concentrated in a limited number of states—Spain, Italy, Germany, and France. On the contrary, the states with a low territorial dimension, like Malta or Luxembourg, are characterized by the over-estimation of flows. The comparative analysis of the two AUF regions suggests that the Erasmus Programme functions in a world-space marked by strong discontinuities, with a rather polycentric structure than a core-periphery model.

The evaluation of the border effect based on the analysis of contiguity between countries indirectly confirms the observations linked to the role played by the academic regions of AUF. It shows that the institutional organization of large alliances of universities can impact the development of academic flows in a way similar to other territorial contexts (e.g., the EU).

The output of the second gravity model (GM2) is synthesized in

Table 3. Effect of the barrier based on the coefficients of regression applied in gravity model no. 2 (GM2).

	2015		2019		2023
Territorial or Spatial Context	Value	Effect-%	Value	Effect-%	Value	Effect-%
DRECO	−0.28	−48.06	−0.10	−19.70	−0.16	−31.04
DREO	0.41	156.48	0.74	444.49	0.59	285.20
Contiguity between states	−0.25	−43.17	0.17	46.63	0.16	44.32
EU belonging	0.46	187.14	0.54	247.25	0.83	575.03

. The values of the effects of the barrier on flows strongly corroborate the observation of the first set of models. In terms of interpretation, the countries integrated in the EU will observe exchanges that are five times more consistent than expected, given the distance and their economic performance, in 2023. This effect is present in all three years we analyzed and increases with a steady rhythm. A similar situation is present in the case of countries belonging to AUF DREO, with fluctuations in the values. Conversely, the states that are members of AUF DRECO will see their interactions reduced by 31%, ceteris paribus (GDP/inhabitant and geographical distance). All the regression coefficients are statistically significant at a p-value of less than 0.01.

The set of gravity models applied in this research was used for the elaboration of cartographic products that describe the macro-structures of Erasmus academic mobility, for the chronological extent we analyzed. The maps reflect the spatial distribution of the models’ residuals and the capacity of flow absorption at the country level. The deviations to the models’ equations (residuals or estimation errors) were classified by implementing a common scale, using a standardization of the values based on z scores, a common practice in the literature [61,62]. Each map output (2015, 2019, and 2023) depicts their distribution operating four classes—underestimated residuals (strong, medium) and overestimated (strong, medium), corresponding to their sign (positive or negative). The class breaks approximate the 98th and the 95th percentiles. Given the large number of flows integrated in the analysis, this discretization will emphasize only those academic interactions that are not sufficiently explained by the predictors of the theoretical gravity model.

In 2015, the spatial distribution of gravity model residuals shows two sets of preferential interactions between countries, the first one concentrated in South-Western Europe (Portugal, Spain, France, and Italy), the second peripheral and including Poland and Türkiye (Figure 2). When added, these two configurations of underestimated flows account for 45.23% of the total number of participants. On the contrary, the overestimated mobility is highly polarized by Luxembourg and Belarus. A few other situations can be detected, like the negative residuals between Romania and North Macedonia, Greece and Malta, and Germany and Lithuania, which confirms our initial hypothesis that the territorial contexts of states explain the patterns of interaction.

In 2019, under the effect of the mobility growth, the residuals map became much more complex (Figure 3). However, despite depicting a more sophisticated network of spatial interactions, the major configurations of flows remain almost identical, especially in the case of the underestimated values of the gravity model. Six countries (Portugal, Spain, France, Italy, Türkiye, and Poland) concentrate 44.8% of the incoming exchanges, a substantial increase compared to 2015. This concentration suggests that a process of “country clubs” might occur in the Erasmus network, with consequences for the Programme’s implementation. The negative residuals (overestimated mobility) maintain almost the same pattern, with two hubs in Luxembourg and Belarus. The major difference when compared with the 2015 map is the appearance of a complex sub-network of under-performing interactions in the Western Balkans, overlapping the states resulting from the dissolution of the former Yugoslavia. The case of insular states like Malta, Cyprus, or Iceland is particularly interesting as it shows that countries with clear features of geographical specificities behave differently within the Erasmus network.

The latest data (2023) used in our analysis confirms the patterns previously observed. The number of significant standardized residuals mapped is much reduced compared to the 2019 situation (Figure 4). This is a consequence of the recovery period that the Erasmus Programme faced after the end of the COVID-19 pandemic, but also due to the perturbations of the project created by the start of the war in Ukraine and the general deterioration of the economic context in the EU over the last years. Despite the turbulence, the major trends in the organization of the system of mobility are stable. The six countries that are systematically labelled as incoming hubs (underestimated flows) reach a ratio of concentration of 47.15% of all the documented interactions (number of participants in the international exchanges), a limited increase compared to 2019. The exceptional negative residuals maintain their spatial pattern, with a trend of concentration in the Western Balkans, island states, and Luxembourg.

To resume, the use of a limited number of predictors (economic performance, distance, and successive territorial contexts) allowed us to extract a set of key findings about the functionality of the Erasmus Programme, using the perspective of academic interactions only. These results underline the fact that mobility is equally shaped by classic factors (economy or distance) and more subtle ones (countries’ integration in different macro-regions or forms of territorial organization). Their combination led to the emergence of potential country club structures of superior attractiveness in the network, while other regions and states exhibit constant patterns of underperformance. In terms of policy design, the relevance of these observations is important for the inherent reforms that the Programme will implement in the future.

4. Discussion

The implementation of the gravity models, one designed to detect the role played by the different territorial contexts of states, the other used to establish the configurations of residuals in these contexts, leads to the elaboration of a set of key findings and potential policy implications for the Erasmus Programme and AUF. The results obtained in our investigation clearly indicate that the network of flows we analyzed is subject to different distortions induced by the possibility of a country belonging to the EU, to one of the AUF bureaus, or by the presence of borders. Also, the residual sums reveal that the intensity of these distortions to the gravity model can be hierarchized. According to these sums, the most intense and positive effect on the interactions is the EU integration, followed by membership in the AUF DREO. The border effect plays a less significant role, being negative in 2015, moderately positive in 2019, and 2023. From the analysis of both GM1 and GM2, one can observe that states belonging to AUF DRECO deploy interactions that are influenced by this territorial context. The explanation for this situation is provided by the heterogeneity of AUF DRECO, including countries both from the EU and its neighbourhood and with different regimes of frontiers’ crossing. The second key finding is related to the predictors’ impact on Erasmus mobility. The datasets analysis and the gravity models systematically emphasize the fact that the economic performance of states is extremely important in the evaluation of the spatial interactions, especially the GDP/inhab. of the destination countries. Given the socio-economic path of students on the labour market, it is possible that the GDP/inhabitant at destinations is correlated with broader opportunities to find jobs or start careers [63,64]. The distance between Erasmus countries remains a significant factor in the decline of mobility. At the world scale, the datasets we analyzed suggest that it is maybe the most important factor (Pearson’s correlation coefficient of −0.54, in 2023, valid for a p < 0.01, number of participants vs. distance between states). However, when the interactions are reduced to the intra-EU flows, it drops to 0.2 (same year, p < 0.01). The intensity of the role played by distance varies in time, integrating different stimuli on the mobility—COVID-19 closure, diffusion of low-cost air companies [65], war in Ukraine, and the financial incentives of the Erasmus Programme, like the green mobility grants [66]. Analyzed at the national level, the distance impact on mobility might not always exhibit a constant morphology [41] of decay, violating in some cases the assumptions of the gravity model.

The key findings observed in the analysis of the barrier effects and their linkage to the territorial contexts of countries’ partners in the Erasmus Programme have policy implications, both for AUF and for decision-makers in the academic environment. The combination of the territorial frames integrated in the gravity models (EU, AUF bureaus, or states’ contiguity) and their differentiated impact on the academic interactions can be used to define new strategies for connecting universities at different spatial scales. In terms of incoming flows, six countries (Portugal, Spain, France, Italy, Türkiye, and Poland) concentrate 47.15% of the mobility in 2023. If one adds the ratios for Germany, the Netherlands, Belgium, and Czechia, the value will increase to 66%. The share of the other state members in the Programme (133) remains one-third. From this short list, only Türkiye is outside the EU, six are members of AUF DREO, and only one is from AUF DRECO. Given the intensity of the concentration, it is important to encourage the emergence of a more polycentric design of the Erasmus network. In the same vein, the discussion of the gravity models’ predictors (GDP/inhab. and inter-country distance) suggests that both the economic performance of Programme members and the geographical separation should be at the core of new strategies of enlargement for the Erasmus exchange, in its future frames. For example, the common financing of transportation costs for mobility is based on distance bands, calculated using the Euclidean formalization (circular distance bands). This method might need revision as it does not integrate the universities’ connectivity by normal transportation modes (air, rail, and roads). It also reflects poorly on the complexity of reaching a remote destination like Cyprus, Malta, or Iceland.

Understanding the complexity of the Erasmus network of interactions is not possible without taking into account more complex factors, particularly those related to the representation of the destinations by students and academic staff. For example, the linguistic affinity between countries might act as a filter for the mobility, subtly encouraging universities with a strong emphasis on English teaching, or with educational offers in the candidates’ mother tongue. Integrating this linguistic affinity in the model is theoretically possible, but the data is still under construction. Similarly, one can introduce predictors such as the destination image or even climate variables. However, when tested, their capacity to globally explain the flows is rather low. For example, the high concentration of positive residuals in Mediterranean countries, like Spain and Italy, can be associated with the specific regional climate (Csa, Csb, Csc, in Köppen classification) and used as a working hypothesis. After testing, the analysis for 2023 shows that only 30% of the flows have destinations in Southern Europe (latitudes lower than +43.3 degrees of latitude, e.g., Marseille, in France). As a matter of fact, 50% of the interactions will concentrate on rather temperate climates (between 45 and 56 degrees of N latitude, e.g., on an illustrative fringe between Milan and Edinburgh). Also, it is important to note that the different territorial contexts used in the model overlap with the aforementioned linguistic and climatic factors, making it difficult to separate their roles in the construction of the Erasmus interactions network.

AUF, as the most important alliance of academic and research facilities in the World, is also concerned with some components of the results obtained in this evaluation of the territorial contexts and their impact on mobility. The analysis of the negative residuals obtained by the gravity models shows that they tend to concentrate in high numbers and with a strong intensity in one of the most challenging AUF regions—DRECO (Eastern and Central Europe). Even if the Erasmus flows used for this paper might not reflect how sophisticated other forms of academic interactions truly are inside DRECO, they still signal the fact that the bureau is facing a set of challenges that need to be addressed. Being a heterogeneous region, we consider that a new agenda of AUF priorities, based on country-tailored solutions and strategies, might counter the potential level of exchanges. The results confirm the initial assumptions and clearly indicate that the academic mobility in the Erasmus space is distorted by the different territorial contexts, with an intensity that varies in time. They also underline the fact that, even within the AUF Regions or intra-EU, the interactions create spatial structures that might be assimilated to “state clubs”, given the volume of some privileged flows. On the contrary, when mapping the negative residuals, one can observe a deficit of mobility in certain key geographical areas, including Europe, the Western Balkans, and the Eastern Mediterranean Region.

In the frame of this study, the implementation of the gravity models and the evaluation of the effects of barriers induced by the countries’ territorial, economic, political, and academic contexts have limitations. The most important one is related to the lack of qualitative variables in the modelling process, at the national scale (linguistic affiliation, historical ties, or cultural background) [67]. Using these variables in the models could increase the explanatory power of our approach, as measured by the coefficient of statistical determination (R2). Also, this study ignored the potential explanations of interactions induced by the field of study and the universities’ specializations. Finally, a more in-depth literature review is needed to determine if the coefficients of interaction’s barrier are consistent with those obtained in studies describing the forms of impedance on economic trade, at least at the scale of the EU and its neighbourhood.

5. Conclusions

This research confirms that the dynamics shaping academic mobility promoted by the Erasmus Programme are complex, and that gravity models, even after the integration of barrier effects for staff and students exchanges, are not able to encompass all the potential factors affecting the interactions at the national level. From the perspective of our analysis, despite the undeniable success of the Programme, there are some latent concerns regarding the concentration of flows in a limited number of countries. This aspect is visible in both the residual maps and the model output. Lacking an explicit decisional implication, there is a risk that this trend of concentration will become stronger year after year. We also show that the overlapping integration of states in different territorial contexts (academic, economic, or political) has nuanced effects on the mobility. In some cases, like the double belonging to AUF DREO and the EU, this overlap has a strong and positive effect on the observed flows. Being an AUF DRECO member has an opposite impact, at least from the angle of view of the gravity models’ residuals. The fact that the effects we measured are stationary in time, at least for the period we analyzed (2015–2023), adds a new layer of questioning regarding the functionality of the Erasmus Programme.

Our approach insisted on revealing the role played by different territorial configurations in the decline of the Erasmus interactions. The workflow implemented follows a double methodological direction. In a first instance, the data needed to be accommodated to some basic GIS demands (mapping the flows, joining country indicators like GDP, and ensuring that all the territorial barriers are coded inside the basemaps). The second direction shifted the workflow from data management to geostatistical analysis. Achieving this objective was possible by using two forms of gravity models, adapted to the needs of our exploration, measuring the effect of the barrier on the Erasmus flows. The overall quality of the models is moderate when one takes into account the values of the R2 (coefficients of determination). However, given the limited number of indicators (only distance between countries and economic performance being taken into account), we consider that the statistical adjustment by gravity models is rather good. Even in these circumstances, the effects we detected are relevant and provide some new insights into how the Erasmus Programme functions and what elements of collaboration might need policy responses.

Compared to previous studies dedicated to the exploration of the Erasmus network of interactions [8,21,27,28], this research underlines the importance of introducing the territorial context (EU integration, large academic alliances like AUF, and distance between states) as a geographical frame for the flows analysis. The economic performance at the country level is a key predictor for the exchanges, and it is highly used in the gravity models studies, as the available literature illustrates. However, its impact is more nuanced due to the territorial filters integrated into this study. This methodological approach shows that the Erasmus flows are also subject to the macro-regional organization of emitters and receiving states, besides their internal descriptors—language of study, higher education territorial endowment, or the spontaneous emergence of collaboration networks between universities.

The paper opens a set of new avenues of research on academic mobility, but due to data access, they limited to the European space mainly. One potential direction is given by new forms of distance conceptualization in the gravity model we applied, by changing its metric (time or cost). The second approach would involve a multi-scale analysis of Erasmus mobility, focusing on the interactions that take place at sub-national levels—NUT3 and NUTS2. We suspect that the predictors will have a scale-dependent behaviour and that the effects on the interactions will be much more limited. Finally, from a methodological point of view, exploring these territorial frames will present interesting new tools for validating gravity models, such as the spatial autocorrelation of flow residuals. This is a trivial problem when dealing with points or polygons in ordinary least squares regressions, but it presents a challenge when addressing the spatial interactions [68]. Finally, from a comparative perspective, it will be of interest to evaluate the coefficients of barrier obtained in this paper with similar studies applied to different forms of spatial interactions (e.g., trade flows). If there is a strong and statistically significant similarity between the two types of barrier effects, one might consider that a structural trans-scalar model of spatial interactions is at work, affecting both economic and academic flows.