2.1. Advances in Visualizing and Understanding Graphs and Complex Patent Networks
Graph theory began in 1736 when Leonhard Euler encountered the Konigsberg bridge problem [
14]. Konigsberg was a city in former Prussia in the 18th century, now called Kaliningrad (Russia), where there were two islands that, together with the mainland, were connected by seven bridges. In the city, there was a discussion about crossing all the bridges without repeating them. However, Euler, in 1736, showed the solution to this problem using simple reasoning: he transformed the bridge paths into straight lines and their intersections into points, possibly creating the first historical graph [
14]. From this, Euler realized that it would only be possible to cross the entire path by passing each bridge once if there were at most two points from which an odd number of paths were left. This idea was based on the fact that, at each point, there should be an even number of paths representing the arrival and departure. The two points with odd paths would refer to the beginning and end of the route, as they would not need a path to arrive and a path to leave, respectively.
From 1970 onward, graph theory had a great leap with the accelerated development of computers, which, after the Second World War, reached their peak with the creation of the first microcomputer software created by students William (Bill) Gates and Paul Allen, which was an adaptation of BASIC for the ALTAIR personal computer designed in 1975 [
15]. Years later, Gates and Allen founded Microsoft, one of the most successful companies in the world. Then, publications referring to graph algorithms appeared, thus opening up possibilities for applying graph theory.
From the aforementioned application, it can be established that a graph
G =
G(
V,
E) can be defined as a structure where
V is a discrete, ordered set of points called vertices,
E is a set of lines called edges, and each edge is connected to at least two vertices. Graph representation can facilitate understanding and problem-solving by allowing lines to connect points [
16]. In this way, maps that represent the organizational structure of a company, routes of transport, communication networks, product distribution, and the chemical structure of molecules can be expressed through graphs. In general, the study of graphs has been growing in recent decades due to the advancement in new computational technologies, which allow for the resolution of problems via algorithms with greater efficiency, speed, and confidence [
17]. Thus, the growing applicability of this theory is a positive factor for social development. One of the practical models that deserves to be highlighted is the problem known as coloring, which can be used in situations that require the selection of elements into independent sets with common characteristics.
In this way, graph theory has proven to be effective in examining and analyzing complex systems, and thus, it has naturally become a highly nuanced topic in the field of patents. Such studies prove that scientific research combining graph theory and patents has progressed, allowing for the viewing of different aspects of patent analysis and visualization from a new perspective. The contribution was made by Gross and Yellen [
18], who provide a purely informative recap of graph theory and its multi-field uses.
Ma et al. [
19] provide a graph-theoretic method for visualization and automated patent analysis in their research. Their experimental work was formulated to test two hypotheses—market covering and competitive threat—using import network and competitive import network as proxies. In addition, the authors incorporated endogenous network structure statistics, node attributes, and external relational network covariates into the models to explain the ever-increasing number of foreign patents worldwide.
Yang et al. [
20] report a network analysis to provide several insights concerning the structure and evolution of international technology diffusion. Furthermore, the demonstration of network analysis effectiveness in delineating clusters of nations that facilitate, moderate, or assimilate patented innovations illustrates the countries responsible for transitions at the cluster level in these networks. Accordingly, by an extensive literature review, they point out broad applications of graph theory, addressing problems like patent citation cases, connectivity mapping of technology, and innovation dynamics [
21].
Moreover, graph clustering algorithms have been observed in creating patent networks, providing a more profound insight into the connections between patents and companies, thereby enhancing the decision-making processes within various organizations [
22]. Additionally, graph embedding techniques have been applied to comprehend the competitive dynamics between firms using patent networks, surpassing traditional topic modeling methods and effectively grouping organizations based on implicit competitive relationships [
23]. Furthermore, there have been proposals for graph representation strategies to automatically extract semantic data from patents, offering semantic assistance for intelligent patent analysis by identifying frequent subgraph patterns and developing text classifiers [
24].
The application of graph theory to large-scale patent datasets presents several challenges. The first is the complexity of understanding patents due to their technical nature, making it difficult to extract relevant information efficiently [
25,
26]. Additionally, the rapid growth of patent documents, characterized by the 3 V aspects of big data (volume, variety, and velocity), further complicates the analysis process [
27]. Moreover, existing approaches like text mining and keyword analysis for patent similarity calculations have limitations, as they rely heavily on word choice and writing styles, potentially leading to inaccuracies in measuring patent relatedness [
28].
Hence, visualization techniques play a crucial role in enhancing the comprehension of patent networks by providing a clear and insightful representation of the relationships between patents and technologies. Using data mining and deep learning approaches, researchers can construct large patent networks exhibiting the intricate connections between patents [
22]. These visual analytics methods enable the visualization of patent portfolio strategies, aiding in identifying similar technologies and the protection of intellectual property rights [
29].
Accordingly, interactive visualizations are crucial for enhancing the understanding and utilization of patent networks. By employing deep learning approaches to construct graph models representing relationships between patents [
22], interactive visualization enables decision-makers to gain precise insights into technological areas and companies, aiding in improved managerial processes within organizations.
Additionally, the application of network mapping and filtering techniques helps remove weak links within the patent network map, thus improving the explanatory power of the network on inventor and organization diversification paths [
30]. Furthermore, network representations allow for comparing molecules from patents with other bioactive compounds, facilitating the exploration of structure–activity relationships and enhancing the understanding of patent information within the broader bioactive chemical space [
31].
All of these works exemplify graph theory in its fundamental form within the studies of patents. Therefore, this concept was subsequently applied to facilitate the extraction of valuable insights, thus enhancing intellectual property analytics. Consequently, overcoming the challenges requires innovative methods, like graph-based patent search engines and novel similarity measures that leverage direct and indirect co-citation links between patents [
32].
Moreover, many network properties describe how nodes are connected to one another and the network as a whole. For instance, centrality represents a fundamental principle in network analysis. It is a metric that quantifies a node’s centrality within the network structure. This metric is a proxy for assessing a node’s significance within the network framework. Below is a
Table 1. comparing different studies and limitations.
This metric began to be investigated during the 1950s and 1960s with several experiments, starting with those carried out under the direction of [
33,
34], who identified considerable differences in the character of group problem-solving activities between different communication structures. Of particular importance was the relationship between the centrality of an agent and its influence on the group. Leavitt [
33], for example, demonstrated through different types of communication structures that the differences in influence between the most central and the least central agent increased with the increasing hierarchy of structures.
Freeman [
35] developed a measure of network centralization based on the difference between the centrality of the most central unit and that of the other units. The rapid development of network analysis in recent years has led to the resurgence of experimental and non-experimental research into the relationship between the centrality and power of social agents.
Nevertheless, what constitutes centrality is subject to variation contingent upon the specific application and perspective being considered. Consequently, there exists a multitude of methodologies for quantifying the centrality of a node. Within the scope of this discourse, four distinct categories of centrality are examined: degree centrality, closeness centrality, betweenness centrality, and cross-clique centrality [
36]. In this article, we focus only on the use of degree centrality, since it is a metric that only considers the number of edges in each node and, thus, provides us with useful information on how important an IPC is in the production chain. The other measures of centrality have shown no insightful information for the acyclic, undirected graph that was built.
Degree Centrality
Secondly, degree centrality is measured based on the degrees in a graph. It can be summarized by the number of neighbors a vertex has, which is important [
37]. According to Freeman’s general formula to compute degree centralization [
36], degree centrality
in an undirected graph is given by:
where:
is the degree centrality,
is the degree of node v,
v* is the vertex with the highest degree,
.
If the network is spread out, then there should be low centralization. If the centralization is high, vertices with large degrees should dominate the graph.
2.2. A Synthesis of Feedstocks and Production Pathways
Global conditions are changing rapidly due to three of humanity’s greatest concerns of this century: the environment, the energy supply, and the global economy. Although they may seem quite distinct initially, these three areas are completely interconnected. The first two have been among the concerns of ordinary citizens for a longer time due to the greenhouse effect and global warming caused by the use of fossil fuels. As for the economy, only time will tell what permanent effects macroeconomic movements will have on the energy sector and, even more difficult to predict, on the environment. The only certainty is that these three sectors will be permanently affected by the use of fossil fuels.
Considering humanity’s concerns in the current century, the necessity of increasing the use of biofuels in a sustainable future offers significant economic and environmental benefits. Biofuels, such as biodiesel derived from organic sources like vegetable oils and animal fats [
38], have the potential to reduce greenhouse gas emissions, improve air quality, promote local agriculture, create job opportunities, and enhance energy security by decreasing reliance on fossil fuels [
39].
Policy measures are crucial for maximizing these benefits through incentivizing biofuel production, ensuring consistent quality standards, and promoting international biofuel trade to enhance economic welfare [
40]. Collaboration between industry and policymakers is essential to optimize biofuel production processes, explore alternative feedstocks, and address challenges like land use competition with food production, ultimately contributing to a more sustainable energy landscape [
41]. Consequently, by aligning policies with industry efforts, biofuels can play an important role in a greener future while fostering economic growth and environmental preservation.
As climate change concerns intensify, there is a greater push for alternative energy sources and ways to mitigate human-made greenhouse gas (GHG) emissions. Amidst all economic sectors, aviation is perhaps one of the most challenging industries to make more environmentally friendly due to numerous technological, economic, and political constraints. Today, it is possible to divide alternative aviation fuels (AAFs) into drop-in fuels, usually what the SAF abbreviation refers to, and alternative propulsion methods like hydrogen or electric propulsion [
10].
According to Cabrera and Sousa [
10], the second group, although promising, is not as viable as drop-in fuels, as it depends on structural changes in airplanes and more investments in research and development. Technologies based on hydrogen, particularly power-to-liquid processes, rely on advancements in green hydrogen production to close the cost gap with fossil sources, while battery power still requires significant research and development funding due to its current lack of technological readiness for commercialization. Without revolutionary breakthroughs, hydrogen- and battery-powered aircraft may have limited scope, primarily suitable for short-range flights. Once technological barriers are overcome, these two pathways are expected to play a vital role in decarbonization.
The drop-in fuels (referred to as SAF from now on) have a more optimistic scope of applicability since it is possible to blend them with traditional jet kerosene and since they are compatible with current aircraft engines and airport infrastructure [
42]. The first flight test using SAF was performed in 2008 [
10] and, currently, only seven SAF production conversion processes and technology platforms have been approved under ASTM D7566 for commercial use, which is shown in
Table 2. Another one was approved under ASTM D1655, a shorter pathway that allows only a smaller percentage of blending.
As shown in
Table 2, there are seven methods approved under ASTM D7566 for producing SAF, using a wide combination of feedstocks. Each of the production methods involves specific processes to convert these feedstocks into jet fuel. For instance, FT-SPK uses gasification and Fischer–Tropsch synthesis, while HEFA-SPK relies on the hydroprocessing of triglycerides. HFS-SIP employs microbial conversion, and ATJ-SPK involves a series of chemical reactions like dehydration and hydrogenation. The table also notes the year of approval for each pathway, ranging from 2009 for FT-SPK to 2020 for the latest methods, such as CH-SK and HC-HEFA-SPK. This highlights the evolution and diversification of SAF production technologies over the past decade, indicating a growing emphasis on utilizing various feedstocks and advanced chemical processes to create sustainable jet fuels.
Although the use of SAF has grown, alternative fuels account for less than 0.1% of jet fuel consumption and cost up to twice as much as its traditional pathways [
44]. There are many barriers to the broader use and development of these technologies, such as economic viability, development difficulties, and legal and bureaucratic issues. To certify a new aviation fuel for commercial use, the contender must endure a three-phase, four-tiered testing process, conducted by the American Society of Testing and Materials (ASTM), which costs at least USD 5 million and takes 3 to 5 years to complete [
10].
The meticulousness of the process is a necessary measure to ensure safety, but it discourages new assets in the field, which can only be encouraged by government measures such as tax subsidies or direct investment programs. Certain institutions follow a pathway of setting goals for the blending of sustainable fuels with conventional ones, but records show that it is more effective to impose a blending mandate than a voluntary approach.
Other alternatives to mandates are policy instruments based on GHG intensity reduction targets, e.g., carbon taxing and carbon marketing [
42].
Considering mechanisms for production, we consider that biofuels are a type of fuel produced with biomass, an organic, non-fossil raw material [
45]. SAF, ethanol, biodiesel, and biogas are examples of biofuels, which are produced with crops such as sugar cane, soybeans, corn, animal fat, and gases from the decomposition of organic materials, such as methane [
46]. In this way, biofuels are made from organic and renewable raw materials, meaning they are recycled and not finite, in addition to there being a wide variety of materials that can be used in the manufacture of these fuels [
47]. This is, therefore, one of its main advantages.
Linked to the renewable aspect of biofuels is the fact that they emit fewer polluting gases into the atmosphere when used to generate energy, which makes them an important alternative source to fossil fuels derived from, for example, petroleum, which generates gaseous waste that contributes to the degradation of air quality in the short and medium term and to the greenhouse effect, which in the long term worsens global warming and causes climate change [
48]. Another advantage for the end consumer is its production cost, which is lower than fuels such as gasoline and diesel.
Like other types of energy-generating sources, biofuels have their disadvantages. Although their burning produces fewer greenhouse gases than fossil fuels, the biofuel production process, which generally takes place in plants or industries, is responsible for releasing polluting waste into the air and water, as is the case with vinasse derived from the distillation of sugar cane, which makes it disadvantageous [
49]. In relation to the biofuel production process, some of them, such as ethanol, require very large amounts of water, one of the reasons why plants are installed close to rivers or dams [
50]. In the case of fuels derived from vegetables such as sugar cane, corn, and soybeans, for example, there is the formation of monocultures specialized in these crops, which can lead to the deforestation of large areas to replace the natural cover with crops, as well as other structural problems, such as land concentration [
51].
Apart from technology, another important aspect to examine when considering SAF production is the ability to scale feedstock production to meet predictions. The primary challenge is maintaining sustainability and avoiding using land designated for food farming. Despite this, SAF feedstock offers several advantages over crude oil, including sustainability, carbon dioxide recycling, renewability, eco-friendly technology, and reduced dependence on petroleum-supplying countries [
52].
As of today, the main alternatives to producing biofuels for jets are non-food energy crops (such as
Camelina, halophytes, and
Jatropha), algae, municipal and sewage wastes, waste wood, forest residues, and fats, greases, and oils (FGOs) [
52]. Some of these options have other positive side effects that can make implementing them more advantageous. Halophytes, for example, can help revert desertification, as they take the salt out of the land when growing [
10]. The employment of waste, especially municipal solid waste (MSW), to produce fuel also addresses environmental concerns associated with landfill decomposition and contamination of soil and water bodies. Despite these benefits, the availability of MSW as an SAF feedstock remains a potential limitation, possibly falling short of meeting market demands [
42]. Algae plants are another profitable opportunity since they reproduce very fast and can help clean polluted water, but the management and lipid extraction of these plants are still a challenge in scalability [
52].
The potential of SAF to reduce GHG emissions varies greatly (between 20–95% when compared to traditional petroleum jet fuel) [
42]. Using vegetable oil as feedstock, for example, is not the most efficient way to decrease GHG emissions due to indirect land use change (ILUC) emissions stemming from increased land conversion for jet fuel production, which competes with the food sector and road biofuel applications [
42]. Apart from the feedstock, technology is an important part of GHG emissions. Forest residues have the lowest GHG emissions when used in Fischer–Tropsch (FT) synthesis but the highest when used in the alcohol-to-jet pathway [
42,
53].
Currently, the HEFA route is the one that has shown better results and has been responsible for the absolute majority of sustainable fuel production hydrocarbons. The main advantage of the route is the existing domain over the technology involved. On the other hand, lipid precursors’ cost, availability, and sustainability represent a major challenge. Furthermore, biofuels produced by the HEFA route are formed by linear alkanes with a boiling point in the diesel range. In this way, if the objective is employment in aviation, additional hydroprocessing is needed to adjust properties. This means that the production cost of HEFA-SPK is currently around three to six times that of conventional aviation kerosene.
From an economic perspective, comparing different routes for producing SAF reveals varying figures for the minimum fuel selling price (MFSP). The average MFSP of the HEFA route is the lowest, at a medium of USD 1.25 per liter. The low prices are justified since HEFA has the greatest production yield, exceeding 1000 liters per ton of dry feed, and relatively lower capital costs, approximately USD 0.34 per liter. The FT and ATJ routes exhibit similar average MFSPs at USD 1.98 and USD 1.86 per liter. The highest average MFSP is observed in the hydroprocessing of fermented sugars (HFS) route, with a range starting at USD 4.56 per liter [
42].
Notably, the choice of feedstock and technology significantly influences the MFSP. For instance, using palm fatty acid distillate as feedstock in HEFA provides an estimated MFSP of USD 1.07, while Pongamia is estimated at USD 5.02 per liter. Employing energy crops in FT synthesis leads to a higher MFSP of USD 2.15 per liter compared to utilizing municipal solid waste (MSW) or forest residues, which yield USD 1.53 and USD 0.92 per liter, respectively. In the case of ATJ, energy crops result in the highest MFSP at USD 2.77 per liter, surpassing the costs associated with sugarcane, agricultural residues, and corn grains, which stand at USD 1.86, USD 2.71, and USD 1.86 per liter, respectively [
42].
Additionally, the gasification-FT route requires substantial investment, where capital costs contribute 50–75% to total production costs, unlike the ATJ route, which ranges from 20–50%. However, despite its higher capital intensity, the gasification-FT route benefits from lower feedstock costs, accounting for 10–35% of total production costs, compared to 15–60% in the ATJ route [
42].
Hence, based on the factors described above, HEFA stands out as the most advanced commercially available fuel production path, as the others still need further refinement, particularly to drive down production costs. Nevertheless, the FT-SPK process is rapidly advancing. It presents notable advantages, such as more feedstock flexibility and the ability to utilize a wide array of sources, such as agricultural waste or MSW, while delivering significant reductions in greenhouse gas emissions.
Accordingly, biofuels hold the potential to create new markets and opportunities; therefore, the integration of SAF encounters significant hurdles, both economically and within regulatory frameworks. Economically, the production of SAF competes for crucial resources such as land and clean energy, thereby impeding its widespread utilization [
54]. Regulatory obstacles encompass the need to blend mandates and consider electricity costs in SAF production facilities [
55,
56].
To surmount these impediments, policymakers can implement supportive measures such as mandatory quotas for SAF utilization and financial incentives directed towards SAF production [
56]. Furthermore, fostering research into alternative pathways for SAF production and addressing concerns regarding SAF’s impact on ice formation in aircraft fuel systems can bolster safety and efficiency, thus promoting greater acceptance of SAF within the aviation sector [
57]. The broader adoption of SAF within aviation can be facilitated through targeted policies and technological advancements to mitigate economic and regulatory challenges.
The United States stands out as a leader in the development of sustainable aviation fuel (SAF) technologies [
58,
59,
60]. Patent data reveals that the U.S. air transport industry has obtained many technological patents for climate change mitigation, particularly inefficient propulsion technologies [
61]. Regarding policy and initiatives, the U.S. has federal rules defining greenhouse gas emission reduction standards for airplanes. It relies on federal, state, and regional voluntary programs for SAF adoption [
62]. Additionally, states like California, Oregon, and Washington have implemented programs allowing SAF producers to participate, further highlighting the U.S.’s commitment to advancing SAF technologies.