Title: From pen and paper to Artificial Intelligence: A history of network science.
Ensovoort, volume 43 (2022), number 7: 1
Network science usually traces its roots to the 1700s, but it was mostly developed during the twentieth century, with a marked explosion during the past two decades. The current article traces network science’s development from early experiments to contemporary integrations with Artificial Intelligence (AI), taking into account key publications and developments in sociology, anthropology, graph theory, economics and military intelligence. The article shows how network science built upon key breakthroughs, adapted to the changing technological landscape, and became a truly interdisciplinary scientific effort. The article also touches upon recent developments in integrating AI with network science, which suggest promising future research avenues.
Keywords: systems; complexity; social network analysis; graph theory; artificial intelligence; complex networks
As shown in previous studies (Senekal, 2021a, 2021b, 2021c), network theory can be considered to be a continuation of Ludwig von Bertalanffy’s General Systems Theory (GST), and was regarded as a component of GST by Von Bertalanffy himself (Von Bertalanffy, 1969:21, 90, 1972:416). Like GST, network theory is interdisciplinary by nature, and the interdisciplinary applications of network theory are reflected by its various roots, ranging from the mathematical to the sociological and anthropological. However, previous discussions of the origins of network theory focus on one development root or another. Freeman (2004), Prell (2011) and Cornelissen (2019) for instance focus on the sociological roots of network theory, while Amaral and Ottino (2004) focus on the development of graph theory. In addition, while Cornelissen (2019:20-23) notes how physicists working within graph theory often disregard the sociological and anthropological roots of network theory, most histories of network theory neglect the military intelligence branch and more recent applications of Artificial Intelligence (AI). The current article aims to provide a more diverse history of network theory that takes various roots into account.
The current article discusses the development of network theory to what Barabási (2002, 2011, 2013, 2016) calls network science, which has developed into a scientific approach in its own right. As such, the current study highlights various key developments and publications with reference to the various disciplines that contributed to this field. Suggestions are also made in terms of future research directions.
Network theory is closely intertwined with graph theory, a branch of mathematics, which is also generally considered to be the oldest root of network theory. The development of graph theory is mostly attributed to Leonard Euler’s famous Königsberg bridge puzzle (Boccaletti et al., 2006:177; Hu, 2012:180; Barabási, 2016:41; Cioffi-Revilla, 2017:142), as formulated in Euler (1736). Euler states the problem as follows (quoted in Amaral and Ottino (2004:151)),
In the town of Königsberg in Prussia there is an island A, called ‘Kneiphoff’, with the two branches of the river (Pregel) flowing around it. There are seven bridges, a, b, c, d, e, f, and g, crossing the two branches. The question is whether a person can plan a walk in such a way that he will cross each of these bridges once but not more than once. […] On the basis of the above I formulated the following very general problem for myself: Given any configuration of the river and the branches into which it may divide, as well as any number of bridges, to determine whether or not it is possible to cross each bridge exactly once.
Euler showed that the problem could not be solved – there is no way all bridges could be crossed only once. In the process, however, he illustrated that physical distance had nothing to do with his problem and he was the first to represent a network as a graph (Cioffi-Revilla, 2017:142).
Francois Quesnay’s (1758) study of financial networks is seen as the first network approach to economic systems (Estrada, 2011:400), and follows shortly after Leonard Euler’s Königsberg bridge puzzle (1736). Quesnay conceived of economic systems as an exchange of value in a system where components are interdependent, and most famously sketched this flow using a form of network or graph, which is reproduced and discussed in Coffman (2021).
The twentieth century
Who shall survive? (1934) by Jacob Moreno (and Helen Jennings) was “a signal event in the history of social network analysis” (Freeman, 2004:7). Moreno and Jennings investigated why 14 girls ran away from the Hudson School for Girls in New York in just two weeks, and suggested that the phenomenon had less to do with the girls’ intrinsic characteristics and more to do with their positions in a social network. Moreno used a technique he called sociometry, which graphically represented the social network in what Moreno called a sociogram (Cioffi-Revilla, 2017:144; Cornelissen, 2019:10). Moreno (1934:11) writes that this approach “enquire[s] into the evolution and organization of groups and the position of individuals within them.” Similar to Euler’s Königsberg bridge puzzle, Moreno emphasizes structure over physical distance, where social influence would spread through the connections between the girls.
Moreno’s conception of social networks influencing individual behavior was not an isolated view, for throughout the twentieth century, many sociologists used a systems-theoretic perspective on societies. Emile Durkheim, for example, argued that societies are comparable to biological systems, consisting of interrelated components, and emphasize the structure of the system above the intrinsic properties of the components. Borgatti et al. (2009:892) write, however, that Moreno’s sociometry was a way of making this abstract social structure tangible.
Sociometry is widely regarded as a precursor to social network analysis (SNA), but Freeman (1996, 2004) notes that the roots of SNA are complex and can also be traced back to the works of e.g. Almack (1922), Wellman (1926), Chevaleva-Janovskaja (1927), Bott (1928), Hubbard (1929), and Hagman (1933). Schnelle (2018:49) in turn identifies George Simmel as the father of SNA.
The works of Kurt Lewin were another clear forerunner of SNA (Prell, 2011:24; Cornelissen, 2019:13). Lewin saw the social environment as a ‘field’ (like the later Bourdieu1), which he defined as “the totality of coexisting facts which are conceived of as mutually interdependent” (Lewin, 1951:240). Lewin (1939:889) writes,
Whether or not a certain type of behavior occurs depends not on the presence or absence of one fact or of a number of facts as viewed in isolation but upon the constellation (structure and forces) of the specific field as a whole. The ‘meaning’ of the single fact depends upon its position in the field; or, to say the same in more dynamical terms, the different parts of a field are mutually interdependent.
As far as the social field is concerned, Lewin came to a similar conclusion as Euler had when he tried to solve the Königsberg bridge puzzle, “the social field is actually an empirical space, which is as ‘real’ as a physical one. Euclidean space generally is not suited for adequately representing the structure of a social field – for instance, the relative position of groups, or a social locomotion” (Lewin, 1939:891). Lewin also introduced the concept of the shortest path to sociology (Bavelas, 1948:17), which would become a key issue in later publications by Milgram (1967) and Watts and Strogatz (1998).
Another discipline that would eventually have an important influence on the emerging science of networks was anthropology. Borgatti et al. (2009:893) write,
… building on the insights of the anthropologist Levi-Strauss, scholars began to represent kinship systems as relational algebras that consisted of a small set of generating relations (such as “parent of” and “married to”) together with binary composition operations to construct derived relations such as “in-law” and “cousin.” It was soon discovered that the kinship systems of such peoples as the Arunda of Australia formed elegant mathematical structures that gave hope to the idea that deep lawlike regularities might underlie the apparent chaos of human social systems.
The anthropologist Alex Bavelas (1948) was a student of Kurt Lewin and was the first to introduce the concept of centrality in social networks (Cioffi-Revilla, 2017:143; Cornelissen, 2019:13). Although he intended to define what Freeman (1977) later formalized as betweenness centrality, the measure he developed was closer to closeness centrality, which does not measure control over information in a network such as betweenness centrality, but rather independence from control (Freeman, 1980:585, 593). Nevertheless, Freeman (1980:586) credits Bavelas for his “intuition” that contributed to the future important development of both betweenness and closeness centralities.
Kochen and Pool’s studies in the 1950s led them to define random graphs (Amaral and Ottino, 2004:152) and the identification of what is known today as the small world phenomenon (Watts and Strogatz, 1998; Watts, 2004). Borgatti et al. (2009:892) write that Kochen and Pool speculated on the basis of mathematical models that at least 50% of pairs in a population like the United States can be connected by chains with no more than two intermediaries. Although their work was not published until the late 1970s (e.g. (Pool and Kochen, 1978)), it was widely distributed in pre-print form and is considered a direct influence on Stanley Milgram’s “six degrees of separation” (1967) studies (Amaral and Ottino, 2004:152; Cioffi-Revilla, 2017:144; Cornelissen, 2019:14).
Like Kurt Lewin and Emile Durkheim, Siegfried Nadel (1957) did not see societies as monolithic entities, but rather as a “pattern or network (or ‘system’) of relationships obtaining between actors in their capacity of playing roles relative to one another” (Nadel, 1957:12). Nadel’s work was one of the earliest formal treatments of the subject of social networks and influenced the later work of Harrison White (Prell, 2011:34).
During the 1950s, Leo Katz worked on centrality measures and developed Katz centrality in 1953 (Katz, 1953), which is closely related to Eigenvector centrality (Bonacich, 1987) and PageRank (Brin and Page, 1998) (Cornelissen, 2019:13). Some of his other key publications include Menzel and Katz (1955) and Coleman, Katz and Menzel (1957).
The term social networks first came into use in 1954, when it was introduced by the American anthropologist, J.A. Barnes (Teige, 2013:141; Cioffi-Revilla, 2017:143). In the 1960s, the focus of network research shifted from anthropology to sociology (Borgatti et al., 2009:893). One of the leading theorists in social network analysis was Linton Freeman, who formalized betweenness, closeness, and degree centrality (see (Freeman, 1977, 1979, 1980). However, it was not until the late 1960s and 1970s that SNA developed into a separate field within sociology, particularly at Harvard, where Harrison White institutionalized SNA (Cioffi-Revilla, 2017:144; Schnelle, 2018:49). White worked with many other influential researchers, including Stanley Milgram, and Peter Bearman, Phillip Bonacich, Ronald Breiger, Kathleen Carley, Ivan Chase, Mark Granovetter and Barry Wellman were some of his students (Cornelissen, 2019:15). Granovetter (1973) studied the links that connect different groups in a network and suggested that ‘weak ties’ have a special importance in the dissemination of information in social networks. Borgatti et al. (2009:893) write that by the late 1980s, social network analysis had become an established field within the social sciences, with a professional organization, an annual conference, specialized software and a journal (Social networks).
By the end of the 1960s, Von Bertalanffy (1969:20) noted that computers had opened up new ways of conducting research. Network science also became intricately interwoven with computerised research (Boissevain, 1979:392; Scott, 1996:212; Cornelissen, 2019:18-20), and Scott (1996:211) argues that the development of network theory is directly related to developments in computer software. In 1971, the program SOCPAC I, written in Fortran IV, was introduced (Cioffi-Revilla, 2017:144; Cornelissen, 2019:18). By the end of the decade, Tichy, Tushman and Fombrun (1979:513) name software platforms such as DIP, SocPac, SOCK, COMPLT, BLOCKER and CONCOR, while Haythornthwaite (1996:331) mentions GRADAP, STRUCTURE, UCINET, NEGOPY and KRACKPLOT. Harrison White and Gregory Heil produced BLOCKER in 1971, Richard Alba and Myron Gutmann produced SOCK in 1972, and Alba also produced COMPLT (Cornelissen, 2019:18), while CONCOR was introduced in Breiger, Boorman and Arabie (1975). UCINET was released in the early 1980s by Linton Freeman (Cioffi-Revilla, 2017:145) and GRADAP was developed by Robert Mokken, Jac Anthonisse and Frans Stokman (Cornelissen, 2019:15). In later years, newer software platforms would be developed to deal with the large amounts of data available since the 1990s, as is discussed later in the current article.
The first paper on random graphs was by Solomonoff and Rappaport (1951), although this publication had a much smaller influence on graph theory than the later Erdös and Rényi (1959, 1960) (Cioffi-Revilla, 2017:143). Pál Erdös and Alfréd Rényi (1959, 1960) developed one of the most influential models in graph theory, and their model laid the foundation for network models that would later evolve into the small-world (Watts and Strogatz, 1998) and scale-free (Barabási and Albert, 1999) models. Cornelissen (2019:22) writes that “practically all reviews” in physics start with a reference to Erdös and Rényi.
The view of economic systems as networks also gained ground in the twentieth century. One specific avenue of research was the study of company director networks, with Jeidels (1905) being the earliest example (Takes and Heemskerk, 2016:3). The League of Nations published The Network of World Trade (1942) in 1942, in which international trade is described as, “much more than the exchange of goods between one country and another; it is an intricate network that cannot be rent without loss” (League of Nations, 1942:7). In the seventies, Snyder and Kick (1979) and Steiber (1979) studied global economic interactions between countries as a system or network, and this approach has increasingly gained ground since the 1990s, as is discussed later.
The development of network theory in the twentieth century took place in parallel with the development of methods in intelligence analysis. During World War II, the US and British intelligence communities developed traffic analysis (also known as communication link analysis or movement analysis) (Van Meter, 2002:67; Ressler, 2006:6). Ressler (2006:6) explains,
This technique consists of the study of the external characteristics of communication in order to get information about the organization of the communication system. It is not concerned with the content of phone calls, but is interested in who calls whom and the network members, messengers, and gatekeepers. Traffic analysis was used by the British MI5 internal security service to combat the IRA in the 1980s and 1990s and continues to be used across the world by law-enforcement agencies including the U.S. Defense Intelligence Agency (DIA) Office of National Drug Control Policy.
Schnelle (2018:49) emphasizes, however, the difference between SNA and communication link analysis. Whereas SNA provides an analytical opportunity to quantify and measure relationships between similar nodes (humans), link analysis provides only the opportunity to compare links between nodes of different types. Communication link analysis will, for example, investigate who dialed a telephone number or to whom money was transferred from a bank account, while SNA instead focuses on the links between persons. In other words, communication link analysis predominantly analyses multi-mode networks where several types of nodes are present, while SNA regularly (but not exclusively) provides single-mode network analysis where only one type of node is present.
In 1996, Alta Analytics developed Netmap, which was one of the first commercial software platforms to facilitate link analysis (Van Meter, 2002:70). Netmap was used by amongst others the US Defense Intelligence Agency (DIA) Office of National Drug Control Policy (Van Meter, 2002:70).
Another similar method in intelligence analysis, the Village Survey Method, was introduced in Thailand in the 1960s by an officer of the Central Intelligence Agency (CIA), Ralph McGehee. McGehee used the Village Survey Method to analyse family and community ties around the secret structure of the Communist Party’s local and regional membership (Van Meter, 2002:67; Ressler, 2006:6; Roberts and Everton, 2011:2).
SNA continued to develop in parallel with traffic analysis and the Village Survey Method in the 1960s and 1970s, but by the 1990s, SNA became increasingly intertwined with methods in the intelligence community. Already in 1991, Sparrow (1991) argued that SNA holds considerable value for intelligence analysis, and the attacks on the World Trade Center on September 11, 2001 led to greater interest in SNA from the intelligence community, as is discussed later in the current article.
Big data and the connected age
In the late 1990s, networks became a topic of interest for physicists. The first seminal publication was an article by Duncan Watts and Steven Strogatz (1998), published in Nature, which argued that the small-world architecture of networks – as proposed by Milgram (1967) and Pool and Kochen (1978) – is a universal feature of complex networks and not just of social networks. In other words, power supply networks, metabolic processes, neural networks and other types of complex networks are comparable to social networks in terms of the average number of links that had to be traversed to reach a node from any other node. Network analysis was now more than just SNA: it became a tool in the study of complexity in general. Latapy, Magnien and Del Vecchio (2008:33) refer to a “post-1998” network theory because of the great influence this publication had.
In 1999, Barabási and Albert (1999) published an article in Science, which showed that complex networks are scale-free networks where the distribution of edges follow the power law. Boccaletti et al. (2006:177) write that this article, together with Watts and Strogatz (1998), caused a “wave of activity” in the physics community, which directly led to the popularity of this approach (these two publications are also singled out in Cornelissen (2019:20-21)).
The entry of physicists into network theory in the late 1990s was accompanied by and a result of the information explosion and the era of big data. Since the late 1990s, significantly larger networks have been analysed with millions and even billions of links, representing a new approach in network theory. Earlier studies of social networks were limited to small networks, for example Zachary’s (1977) study of social interactions at a karate club, but the information explosion made it possible to analyse large social networks such as the international film actor network (Amaral et al., 2000; Newman, Strogatz and Watts, 2001; Jeong, 2003; Guillaume and Latapy, 2004, 2006; Latapy, Magnien and Vecchio, 2008; Nacher and Akutsu, 2011; Tumminello et al., 2011). In economics, large networks such as company director networks (Davis, Yoo and Baker, 2003; Conyon and Muldoon, 2006; Durbach, Katshunga and Parker, 2013; Heemskerk, 2013; Heemskerk, Daolio and Tomassini, 2013; Senekal and Stemmet, 2014, 2019; Drago et al., 2015; Friel et al., 2016; Takes and Heemskerk, 2016; Williams, Deodutt and Stainbank, 2016; Drago and Ricciuti, 2017; Raddant, Milaković and Birg, 2017; Guo and Lv, 2018) and networks of global trade (De Benedictis and Tajoli, 2011; Glattfelder, 2013; Akerman and Seim, 2014; Senekal, Stemmet and Stemmet, 2015a, 2015b; Senekal, 2017a, 2020) could now be studied. In linguistics, the structure of language itself could now be modelled as a network (Dorogovtsev and Mendes, 2001; Ferrer I Cancho and Solé, 2001; de Jesus Holanda et al., 2004; Kosmidis, Kalampokis and Argyrakis, 2006; Liang et al., 2009; Cong and Liu, 2014; Ke et al., 2014; Senekal and Kotzé, 2017), as could cultural networks (Gleiser and Danon, 2003; Senekal, 2015, 2017b; Fraiberger et al., 2018; Wang et al., 2019).
Of particular note is the studies by Christakis, Fowler and co-authors (Christakis and Fowler, 2007, 2008; Fowler and Christakis, 2008, 2011; Rosenquist et al., 2010; Rosenquist, Fowler and Christakis, 2011; McDermott, Fowler and Christakis, 2013; Shakya et al., 2016). Using a large dataset, Christakis, Fowler, and co-authors found that behavioral patterns such as obesity (Christakis and Fowler, 2007), depression (Rosenquist, Fowler and Christakis, 2011), divorce (McDermott, Fowler and Christakis, 2013), happiness (Fowler and Christakis, 2008), smoking cessation (Christakis and Fowler, 2008), alcohol abuse (Rosenquist et al., 2010), and violence in intimate relationships (Shakya et al., 2016) spread across social networks. Referring to Christakis and Fowler’s research, Papachristos and co-authors (Papachristos, Braga and Hureau, 2012; Papachristos and Wildeman, 2014; Papachristos et al., 2015; Papachristos, Wildeman and Roberto, 2015; Green, Horel and Papachristos, 2017) found that firearm-based violence also spreads across social networks. In Green, Horel and Papachristos (2017:327), for example, the authors suggest that firearm-based violence also spreads like obesity across social networks through personal contact, and compares the spread to viruses.
This shift to studying larger networks had several analytical implications, including analyzing the network structure rather than the single node’s position in the network, and placing restrictions on the visualization of networks because such large networks cannot always be visualized in a meaningful way. Software developments also facilitated the study of larger networks, such as Pajek (Batagelj and Mrvar, 1998), Cytoscape (Shannon et al., 2003), and Gephi (Bastian, Heymann and Jacomy, 2009). Przulj and colleagues (Przulj, Corneil and Jurisica, 2004; Przulj and Higham, 2006; Kuchaiev et al., 2011) also created GraphCrunch, which facilitates the comparison of different networks, focused on but not limited to biological networks.
Much research has also been focused on the development of faster algorithms such as those of Latapy (2008), Blondel et al. (2008), Cohen et al. (2014), Liu et al. (2017), and Paluch et al. (2018), because calculations now had to be done on a significantly larger scale. Cohen et al. (2014) for instance found that calculating closeness centrality on a network of 23 947 nodes and 28 854 edges would take 44 222 hours or just over 5 years to complete. When analysing large networks such as the world wide web, developing faster algorithms is essential, which also led to the introduction of machine learning, as is discussed later in this article.
Adapting to the ranking of pages on the world wide web, Google founders Brin and Page (1998) suggested PageRank, a measure with which to rank search results, but which also proved valuable in other networks where important nodes were to be identified, such as citation networks. While PageRank was developed for Google, Kleinberg (1999) developed Hyperlink-Induced Topic Search (HITS) for Teoma and Ask.com.
Algorithms for the visualisation of larger networks also progressed from the earlier work by e.g. Eades (1984), Barnes and Hut (1986), Kamada and Kawai (1989), and Fruchterman and Reingold (1991), to newer, faster algorithms such as those by Walshaw (2003), Martin et al. (2011), and Hu (2012), which are capable of handling large networks.
This revolution in network studies does not mean that smaller networks cannot still be analysed: the analysis of large networks yields a different kind of knowledge than the analysis of small networks and especially within the Humanities, smaller networks often offer more meaningful answers. For example, it does not necessarily convey meaning that the link distribution pattern in a network follows either a Poisson or power law distribution, but it may be important that one person has a more advantageous position than another in a small social network. In literary studies, for instance, character interactions have been studied in a variety of publications (Stiller, Nettle and Dunbar, 2003; Stiller and Hudson, 2005; Carolina Sparavigna, 2013; Mac Carron and Kenna, 2013a, 2013b; Senekal, 2019), and these usually involve smaller networks.
The intelligence community also embraced network analysis in the era of big data. Krebs’s (2001) network analysis of the 9/11 hijackers was one of the key publications to highlight the promise that network analysis holds for the intelligence community, which was followed by Kochade’s (2006) analysis of the Bali bombings of 2002. Burcher and Whelan (2018) show that a plethora of academic studies investigated so-called ‘dark networks’ (illegal networks), including Schwartz and Rouselle (2009), Bright et al. (2012), Décary-Hétu and Dupont (2012), Bouchard and Amirault (2013), and Morselli (2013). More recently, Bright et al. (2021) also indicate the growing popularity of social network analysis in the study of dark networks.
This interest in networks by the intelligence community was supported by extensive defense budgets, and the Defense Advanced Research Projects Agency (DARPA), US Army Research Labs, the US Office of Naval Research (ONR), the National Security Agency (NSA), the National Science Foundation (NSF) and the Department of Homeland Security (DHS), funded research related to social network analysis (Ressler, 2006:7). This funding enabled the development of increasingly sophisticated software, and a full integration of intelligence analysis methods with network theory. Numerous software platforms, including Pathfinder, Sentinel Visualizer, and i2 Analyst’s Notebook, were developed around this time, some with funding specifically allocated from the US defense budget (Senekal, 2014:89). By 2006, the US Army and Marine Corps Counterinsurgency Field Manual (Department of the Army and Department of the Navy, 2006:B-10-B-17) included a dedicated section dealing with SNA, where they write SNA is, “a tool for understanding the organizational dynamics of an insurgency and how best to attack or exploit it” (2006:B-10).
Recent developments in Artificial Intelligence (AI), which includes machine learning (ML), opened up new opportunities with which to study complex networks. Quesada et al. (2019:1) write, “Combining complex networks analysis methods with machine learning (ML) algorithms have become a very useful strategy for the study of complex systems in applied sciences.” For instance, they (2019:2) suggest,
… descriptors of complex networks at the local and global scales (degree distribution, average degree, diameter of the network, average shortest path, clustering coefficient, connectedness, node centrality, and node influence) can be used as input variables to train ML algorithms in order to predict the properties of these systems.
One application of machine learning at the global (macro level) scale is Attar and Aliakbary (2017), who use machine learning to classify networks based on their topology. At the local (node-level) scale, Wen et al. (2018), Grando, Granville and Lamb (2018), Zhao et al. (2020), Bucur (2020) and Fan et al. (2020) developed ways in which to use machine learning instead of classic centrality measures to identify important nodes in a large network. Grando, Granville and Lamb (2018) suggest that using machine learning to identify important nodes is a direct result of analysing larger networks, since “typical centrality measures algorithms do not scale up to graphs with billions of edges (such as large social networks and Web graphs).” While still early in its development, integrating AI with network science is a promising avenue for future research.
Network science developed over the past century (with roots dating to the 1700s) with the help of scholars in a variety of disciplines. Today, network science has found applications in most disciplines. The network science community is enthusiastic about network science’s ability to provide new answers to complex phenomena, and Barabási (2011) for instance believes that network science has come to dominate the study of complexity.
The recent development of integrating AI with network science not only testifies to the adaptability of network science in the contemporary scientific environment, but also creates promising avenues of future research. As ever larger datasets are gathered and analysed, AI is sure to develop into a productive partner of network science.
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