Last September, as part of our seminar series, “60 minutes of DH”, at the IEG, I presented an introduction to historical (social) network analysis. In the talk, I gave an overview of the field’s history, discussing landmark papers, in my opinion. It was a mix of going through papers fundamental to shaping the discipline (a kind of consensus in the network science/social network analysis communities) and those that are important to me or I like. In the following, I will recount this biased – based on my opinion – talk about the evolution of networks research in this two-part post.

First, I must say that the use of the term “historical network analysis” is merely to identify the discipline in which we are using network analysis: history. There are no new or different methods or concepts that can distinguish historical network analysis from the traditional field of social network analysis (SNA).

We can trace the use of dots (nodes or vertices) and lines (links or edges) to solve problems back to 1736. That was when Leonhard Euler “solved” the Seven Bridges of Königsberg puzzle (Fig. 1), showing that it was impossible to walk around the whole town (all four pieces of land and all bridges) crossing the bridges only once. His theorem, elegant but simple, laid the foundations of graph theory in mathematics. It stated that there are two conditions for a walk like that – reaching all nodes of the graph using each edge only once – to be possible. First, the graph must be connected, i.e., no part of the graph can be isolated (a node or group of nodes that cannot be reached by other nodes). Second, there can be none or only two nodes whose degree – the number of edges incident to the node – is odd in the whole graph.

Going forward two centuries, in 1934, Jacob Moreno and Helen Jennings used nodes and edges to create what was called a sociogram to represent social ties. In his publication “Who shall survive?: A new approach to the problem of human interrelations” (Moreno 1934), Moreno used the sociogram to study the relationships between kids from kindergarten to the 8th grade (Fig. 2). This study is considered the birth of social network analysis, including network visualization.

On the side of graph theory, Dénes König published the first textbook on the topic in 1936 and, at the end of the 50s, Paul Erdős, Alfréd Rényi, and Edgar Gilbert made essential developments with their work (Erdős and Rényi 1959; Gilbert 1959) on random graphs, where edges connect nodes at random. Their models of random graphs – considered the foundations of what came to be the field of network science – gave the basis for researchers to explore phase transitions and expected properties in the structure of these random graphs. The former is related, for instance, to with which density (existing edges per total possible edges in the graph) we can expect to see small components (groups of nodes disconnected from the others nodes) to start to merge, and create what we call the largest connected component or the giant component (a component containing the majority of nodes of the network).

In terms of properties, their models helped us comprehend the expected degree distributions (how the degrees are distributed among the nodes), average path length (a path length is how many edges are necessary from one node to reach another), and clustering coefficient (the tendency of nodes to form close-knit communities) of random networks, according to the number of nodes and edges in a network. Then, we can compare the properties of empirical networks to those of random networks to identify patterns that emerge when connections are not made at random, thus having underlying mechanisms.

Then, the 70s and the 80s came with many seminal papers on social networks: new theories, new concepts, new models, new metrics. I think of this period as the Golden Age of social networks research. Here, I will highlight (only) four of them.

The first is “The strength of weak ties” by Mark Granovetter (Granovetter 1973) where he drew attention to the fact that social ties (the edges of the network) that appear to be weak, like acquaintanceships rather than friendships, can be better for accessing information. These ties facilitate the diffusion (flow) of things (ideas, innovation, opinions, diseases) on social networks, connecting communities – where strong ties are frequent –, and allowing these things to spread further (Fig. 3). Without these ties, information (or the other things) would stay trapped within isolated communities of people that are strongly connected.

In the following year, Ronald Breiger published “The duality of persons and groups” (Breiger 1974). This paper is significant to my research because it laid the foundations for analyzing and modeling data as two-mode (bipartite) networks. These networks have two types of entities – thus the name “two-mode” – and nodes of one type can only connect to nodes of the other type. Through a method called projection, we can create a new (one-mode) projected network with only the node type in which we are interested (Fig. 4). For instance, imagine creating a (two-mode) network connecting students to courses they take at the university. Then, in the projected network, students are connected if they attend the same course together.

Modeling networks with two types of entities is very common in social systems. As examples, my colleagues and I modeled the spread of Covid-19 in New Zealand (Harvey *et al.* 2020) and explored political networks (Curran *et al.* 2018) based on this concept. Thus, in the last few years, I have studied how the structure of the bipartite network affects the structure of the projected network. If you want to know more about two-mode networks, I wrote a more extensive introduction to the topic in my PhD Thesis (Vasques Filho 2018a).

The third paper I want to highlight from this period is “Centrality in social networks: Conceptual clarification” by Linton Freeman (Freeman 1978). As the name of the paper states, the relevant contribution it made was to clarify what a bunch of proposed metrics of network centralization actually means. With that, Freeman also dismissed many propositions, showing how they were failing to achieve their goal of finding central nodes – those that are somehow more important in the network structure than the others. As a consequence, three centrality measures became very popular. First, degree centrality is the same as node degree (i.e., the number of edges incident to the node). With a high degree, a node has direct access to many other nodes, and that can play to its advantage, of course. Second, closeness centrality gives us an idea of how easily a node can reach – directly or indirectly – every other node in the network. Third, betweenness centrality tells us how likely the node facilitates another node to access others, i.e., if the node is in the shortest path between two other nodes. Nodes with high betweenness centrality can function, for example, as gatekeepers, deciding whether to pass or hold anything that flows in the network.

Finally, the fourth paper is “The focused organization of social ties” by sociologist Scott Feld (Feld, 1981). In this paper, he presented his “focus theory,” built upon the idea first proposed by Georg Simmel that social structure consists of loosely connected social circles. People that belong to different circles create these loose connections. Feld argues that most relationships are created as people participate in activities around a focus, i.e., some social context that draws people to perform an activity together (for instance, a school, a band, a soccer team).

This theory brings another paradigm for understanding social structure: we have to care not only about the individuals in the social network, but also about the collectivities in which they participate! Although Feld did not see it at the time, looking at individuals and social circles is the same as looking at two-mode networks. Part of my current research is putting the pieces of the puzzle created by Breiger (1974) and Feld (1981) together with recent developments on two-mode networks I have worked on (Vasques Filho and O’Neale 2018b, 2020a, 2020b), to create a more comprehensive theory of social structure. I uploaded the first steps of developing such a theory (Vasques Filho, 2020c) here.

To end this part of the post, I want to present another concept: structural holes, developed by Ronald Burt (Burt, 1992). In a nutshell, these holes are missing links between two groups of people (Fig. 5). Then, we have two groups with people densely connected intra-group but with no connections to people in the other group. Burt argues that whoever makes the connection between these two groups could have an advantage, because this person would potentially benefit from the knowledge created by both groups. Moreover, this person plays the role of gatekeeper, deciding which information can pass or not from one group to the other.

By now, you might be thinking that you have heard this before. Yes, we talked about it a few paragraphs above: this person likely has a high betweenness centrality! And not only that, this concept resembles Granovetter’s idea of weak ties. Thus, a person weakly connected to another in a different group (or community) likely scores high in betweenness centrality, and has different sources of information with a certain advantage in relation to others, perhaps increasing her social capital.

Everything we have talked about so far is finally coming together. In the next part, we will discuss when physicists joined network research at the end of the 90s, a seminal work applying SNA to a historical context (finally!), and much more.

### References

- Błoch, Agata, Demival Vasques Filho, and Michał Bojanowski. 2020. “Networks from Archives: Reconstructing Networks of Official Correspondence in the Early Modern Portuguese Empire.” Social Networks. https://doi.org/10.1016/j.socnet.2020.08.008.
- Breiger, R. L. (1974). The duality of persons and groups.
*Social Forces*, 53(2), 181-190. - Burt, R. S. 1992. Structural holes: The social structure of competition. Cambridge, MA: Harvard University Press.
- Curran, B., Higham, K., Ortiz, E., & Vasques Filho, D. (2018). Look who’s talking: Two-mode networks as representations of a topic model of New Zealand parliamentary speeches.
*PloS One*,*13*(6), e0199072.

Erdős, P. and Rényi, A. (1959). On random graphs I.*Publ. Math. Deb.*, 6:290–

297. - Feld, S. L. (1981). The focused organization of social ties.
*American journal of sociology*,*86*(5), 1015-1035. - Freeman, L. C. (1978). Centrality in social networks conceptual clarification.
*Social networks*,*1*(3), 215-239. - Gilbert, E. N. (1959). Random graphs.
*The Annals of Mathematical Statistics*, 30(4), 1141-1144. - Grandjean Martin (2018). Moreno’s Sociograms, Data set, https://github.com/grandjeanmartin/sociograms/. DOI 10.5281/zenodo.1998343
- Granovetter, M. S. (1973). The strength of weak ties.
*American journal of Sociology*, 78(6), 1360-1380. - Harvey, E.
*et al*. (2020). Network-based simulations of re-emergence and spread of COVID-19 in Aotearoa New Zealand. Tech. Rep., Te Punaha Matatini. - Moreno, J. (1934).
*Who shall survive? A new approach to the problem of human*. Beacon, NY: Beacon House.

interrelations - Vasques Filho, D. (2018a).
*Structure and dynamics of social bipartite and projected networks*. PhD Thesis, University of Auckland. - Vasques Filho, D., & O’Neale, D. R. (2018b). Degree distributions of bipartite networks and their projections.
*Physical Review E*,*98*(2), 022307. - Vasques Filho, D., & O’Neale, D. R. (2020a). The role of bipartite structure in R&D collaboration networks.
*Journal of Complex Networks*,*8*(4), cnaa016. - Vasques Filho, D., & O’Neale, D. R. (2020b). Transitivity and degree assortativity explained: The bipartite structure of social networks.
*Physical Review E*,*101*(5), 052305.

*Digital Humanities Lab*, 28/01/2022, https://dhlab.hypotheses.org/2363.

Featured Image: *Correspondence networks in the early modern Portuguese empire*, in: Błoch, Vasques Filho, and Bojanowski 2020, p. 11.

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