Introduction to historical (social) network analysis – Part 2

by Demival Vasques Filho

In the first part of this blog post, we discussed the first studies in graph theory and social network analysis. Then, we introduced several concepts: random networks, weak ties, two-mode networks, centrality measures, the focus theory, network visualization, and structural holes. Now, let us move on to some applications and yet new concepts!

The first seminal work using network analysis in a historical context was “Robust Action and the Rise of the Medici” (Padgett and Ansell 1993). Interestingly, the authors are not historians (instead political scientists) and published the paper in the American Journal of Sociology. Another early historical network study–but much less well-known work–, “Relations into Rhetorics: Local Elite Social Structure in Norfolk, England, 1540-1640” (Bearman 1993), was published in the same year by a sociologist. I am not entirely sure why this is–I find the arguments in “Historical Social Network Analysis” (Wetherell 1998) incomplete. I suspect the primary issue is the narrow-minded majority of history scholars clinging to tradition and disdaining “new” methods (network analysis has been around since the 1930s, as we have seen).

Padgett and Ansell (1993) explored multiplex networks of elite families to explain the rise of the Medici to power and the Florentine Renaissance state-building process. We refer to a network as multiplex when several types of ties connect nodes. In this study, the data enabled the construction of networks with nine types: marriage, partnership, employment, trade, real state, loans, patronage, patronage, and Mallevadori (friends who put up surety) (Fig. 1). Based on how families were connected, the Medici assumed an “extraordinarily centralized” (Padgett and Ansell 1993, p. 1278) position which, in turn, allowed them to concentrate power.

Fig. 1. Networks of elite families in Renaissance Florence. The multiplex networks show the centralized position of the Medici following their ties with other families. Figure extracted from (Padgett and Ansell 1993).

A few years later, physicists boarded the network research boat with two works that became remarkably well-known for introducing fundamental concepts in the emerging field of network science. The first, “Collective dynamics of ‘small-world’ networks” (Watts and Strogatz 1998) presents a model suggesting that networks are, as the title says, “small-world” networks. Observable networks in any system (social, ecological, etc) share two universal properties: low average path length and high clustering, when compared to lattice and random networks (Fig. 2), respectively. Lattice networks have a regular structure, where all nodes have the same number of edges and are connected only to other geographically close nodes. As a result, they present high average path length and clustering. In random networks, as we saw before, nodes are connected by chance and have low average path length and clustering (note: these comparisons hold for sparse networks, where the number of nodes is much larger than the average degree of a node).

Fig. 2. The small-world network model. Starting from a regular (lattice) network, we pick each edge and reconnect it to nodes at random with a certain probability p. The higher this probability is, the closer the network will get to a random network (top figure). As we increase this probability, the average path length decays fast, while the clustering keeps at high values for much longer (bottom figure). Thus, empirical (small-world) networks sit between regular and random networks. Figures extracted from (Watts and Strogatz 1998).

The second, “Emergence of scaling in random networks” (Barabási and Albert 1999), introduced the concept of scale-free networks. To put it simply, scale-free means that we see similar patterns as we zoom in or zoom out when looking at the network connections. In mathematics, we refer to it as fractal–something whose small parts resemble the whole as, for instance, the patterns in broccoli and cauliflower. Empirical networks are considered scale-free because of another universal property: the heavy-tailed distribution of node degrees. Let me translate: independently of the type of network, we tend to see few nodes with many connections and many nodes with few connections.

These paper findings caused a fuss for two reasons. First, they diverged from the mainstream idea among mathematicians and physicists that node degrees were distributed following a Poisson distribution (resembling the famous bell curve) as it happens in random networks. Instead, the heavy-tailed distribution follows the shape of a power-law (hence why power-law is another famous term in network research), as Fig. 3 shows. Physicists were euphoric about this because this type of distribution is found in many situations as, for instance, the distribution of earthquake magnitude, cities’ population size, and wealth and income. Now, they could see the power-law in networks too.

Fig. 3. Degree distributions of random (top left) and scale-free (top right) networks. That reads as the probability of finding a node with a certain degree when taking a node at random. Due to the long tail of the degree distributions of scale-free networks, we usually use logarithm scale to visualize them. In the bottom, examples of the structure of both networks (left: random; right: scale-free). Figure created by the author.

However, the paper’s findings were not exactly new, and that is the second reason it created a fuss and a certain animosity with sociologists, especially those studying social networks. Barábasi and Albert (1999) argued that the preferential attachment mechanism creates such distributions in networks: nodes likely attract other nodes to create edges between them proportionally to their degree. That is, high-degree nodes tend to get even more connections in a rich-gets-richer process. This mechanism, of course, was well-known by social scientists for decades under the terms cumulative inequality or the Matthew effect, but its role on breeding social connections is still unclear. Furthermore, Moreno (1934) had already noticed back then that social networks present this inequality in connectivity among actors. So then, what was actually innovative about (Barabási and Albert 1999)? The probable answers are the use of big data and the universality of heavy-tailed degree distributions in different types of networks other than social ones.

In my view, preferential attachment is not the leading mechanism that results in connectivity (popularity) inequality in societies’ structures. In this text (Vasques Filho 2020)–an incipient theory of population-scale network structures–I argue that these heavy-tailed distributions emerge from a combination of mechanisms, none of them preferential attachment.

More on the topic of mechanisms of network formation, we jump to homophily with “Birds of a feather: Homophily in social networks” (McPherson, Smith-Lovin, Cook 2001). Homophily is the principle in which similar people tend to be in contact and create ties more easily than dissimilar people. The paper puts together a wide range of previous works to build the idea that homophily functions as an organizing principle of social structure. The argument is based on the evidence collected over many years that several homophily dimensions facilitate tie formation among people: race and ethnicity; sex and gender; age; religion; education, occupation, and social class; network position; behavior; attitudes, abilities, beliefs, and aspirations; geography.

When people tend to connect with similar ones (considering the multiple dimensions of homophily), people tend too, consequently, to form clusters or communities. The search to identify community structures in networks can be traced back to (Luce and Perry 1949). However, it only picked up speed in the early 2000s, once again with physicists, especially Mark Newman, who has contributed greatly not only to community detection (Girvan and Newman 2002; Clauset, Newman and Moore 2004, Newman and Girvan 2004, Newman 2006) but to network science in general (Newman 2003,2018). There are several methods (algorithms) for detecting community structure. Independently of the method, their focus is to find groups of nodes in the networks more densely connected among themselves than to other nodes outside such a group (Fig. 4). Nowadays, the most used method is the Louvain method (Blondel et al. 2008), based on modularity optimization. Modularity–introduced in (Newman and Girvan 2004)–is a measure that calculates how well defined the communities are, by estimating the quality of the partition of the network.

Fig. 4. A schematic drawing of how nodes can organize themselves in communities where they are more densely connected to each other than to other nodes outside the community. Figure extracted from (Newman 2006).

We can now leave network structure aside to talk about dynamics on networks (or how things flow on networks) with “Complex contagions and the weakness of long ties”(Centola and Macy 2007). The paper’s title clearly references Granovetter’s (1973) “Strength of weak ties”discussed in the previous post. Macy and Centola (2007) use the term long ties to refer to weak ties – we can think of the latter as those connecting not-so-close acquaintances that ultimately connect socially distant communities. In this paper, they showed that weak ties (e.g., acquaintanceship) can actually be weak in the sense of spreading information, i.e., they might not be sufficiently good information disseminators.

However, doesn’t that contradict Granovetters “strength of weak ties” theory? Well, in parts, yes, depending on the spreading process type. Weak ties can still be strong in a “simple contagion” process, where only one (weak) tie is sufficient to spread something (e.g., information about a job position or a virus like the new coronavirus). Otherwise, a weak (long) tie is not enough for “complex contagion”– a spreading process in which strong ties (e.g., friendship or peer pressure) are necessary for something to flow across actors in the networks. For instance, it is easier for you to change your opinion about something or believe in something (like fake news) if a friend is a source instead of an acquaintance. And even more if many friends (as in peer pressure) are the source. That is, in a complex contagion process something spreads further if flowing through a strong tie and/or flowing from a large proportion of a node’s ego network, the node’s direct network neighborhood (Fig 5).

Fig. 5. A schematic showing the two (simple and complex) spreading processes starting from a seed (source) node. Note how the square node adopts the transmission only after two nodes in its ego-network have done so. Figure extracted from (Min and San Miguel 2018).

Jumping to a historical context, the paper “Multiplex Network Ties and the Spatial Diffusion of Radical Innovations: Martin Luther’s Leadership in the Early Reformation”(Becker et al. 2020) used contagion models to explore Luther’s role in the spread of the Reformation in its early days. For that, the authors investigated two spreading mechanisms. First, under the direct influence of Luther, they inferred the likelihood of a city adopting the Reformation if the city had someone as part of Luther’s ego network (e.g., a former student of his or someone to whom he has written letters) and whether he had visited that city. They calculated such likelihood using both simple and complex contagion. For the former, it is relevant to know if Luther had at least one point of contact with the city (one student, one letter, one visit). For complex contagion, the quantity of those is necessary, i.a. how many students, letters, visits. Second, they also inferred the likelihood of a city adopting the Reformation based on a trade network (i.e., cities are connected if they had a direct route of trade between them). For this case, they used complex contagion models in which a city could adopt the Reformation after a certain proportion of other cities in its direct neighborhood had previously adopted the Reformation. They argue that these processes could not explain the spread of the early Reformation independently; instead, both Luther’s direct (complex) influence and the trade network were necessary for that to happen.

On a final remark, the four authors of the last study on the spread of the Reformation are again not historians. Moreover, the paper was published in the American Sociological Review journal. That is not to say that there are no initiatives to promote social network analysis in a historical context. I want to highlight the brilliant work the historical network research (HNR) community has been doing. The Journal of Historical Network Research, inaugurated in 2017, is an excellent venue and has recently launched its fourth volume. Another example is the bimonthly HNR Lunch Lectures series.

Nevertheless, these are efforts by a small group of people. History as a discipline was one of the last (if not the last) to recognize (and it is still reluctant to do so) network methods as powerful tools to complement traditional methods. As I noted in a post in this blog in 2020, the participation of History institutes and departments representatives in network-related conferences is still very shy. I hope this 2-part introduction to networks research serves as a small contribution to changing that.

See you in a networks conference!


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Cite this article as: Demival Vasques Filho, "Introduction to historical (social) network analysis – Part 2," in Digital Humanities Lab, 04/03/2022,

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

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