Dynamic Network Analysis: 6. What is a network?

A network is an interrelated series of events having consequences affecting the likely repetition of those interactions.

Pail Brigade Porcupine Fire - July 9th 1911 [pkdon50 (https://creativecommons.org/licenses/by/2.0)], via Wikimedia Commons
John Terrell

AS AN ANTHROPOLOGIST WHO FOR DECADES has been studying how we humans deal with one another and the world around us, I find it fascinating that experts writing about networks and network analysis evidently have difficulty using what I like to call relational thinking.

Here again are the definitions of the two modes of thought I offered in an earlier post in this series:

Categorical thinking assumes things exist apart from one another, and may then become connected with one another. 

Relational thinking assumes instead things exist because they are connected.

As evidence of the continuing appeal of categorical thinking even in networks science, here is an answer to the question “What is a social network?” given by David Knoke and Song Yang, two of the leading writers on social network analysis. “A social network is a structure composed of a set of actors, some of whose members are connected by a set of one or more relations” (Knoke and Yang 2008: 8).

Here is another definition, this time by John Scott, also a leading writer in this field, similarly implying that social networks are a particular class of things within the general category called structures. “Social network analysis emerged as a set of methods for the analysis of social structures, methods that specifically allow an investigation of the relational aspects of these structures” (Scott 2000: 38).


In both of these definitions (there are others I could give you), the authors are evidently assuming that there is (1)  a class of things called social structures*  within which (2) people relate to one another in distinct ways making it possible to (3) isolate what they are doing and then label them as “actors” operating within a particular kind or type (i.e., category) of structure.

From the relational perspective I am writing about in this series, however, these supposed structures only exist when—or perhaps I should say throughthe relational acts or events that the identified actors are participating in.

It would be more than simply metaphorical, therefore, to say that networks may have more in common with thunderstorms than with the sorts of things one usually thinks of when somebody uses the word “structure.”

Houses, hotels, banks, and boardwalks are all clearly structures. Why use this word also to talk about social networks?

A little history

Scott has reviewed in some detail the history behind why experts in social network analysis see networks as structures of a certain sort. Put briefly,  contemporary network analysis is rooted in the 20th century development of mathematical graph theory and structuralist approaches to social organization in sociology and social anthropology. As Scott has concluded: “It is undoubtedly the case that social network analysis embodies a particular theoretical orientation towards the structure of the social world and that it is, therefore, linked with structural theories of action” (Scott 2000: 37).

“Johnson’s algorithm is a way to find the shortest paths between all pairs of vertices in a sparse, edge-weighted, directed graph. It allows some of the edge weights to be negative numbers, but no negative-weight cycles may exist. It works by using the Bellman–Ford algorithm to compute a transformation of the input graph that removes all negative weights, allowing Dijkstra’s algorithm to be used on the transformed graph. It is named after Donald B. Johnson, who first published the technique in 1977.” By David Eppstein [Public domain], from Wikimedia Commons (https://en.wikipedia.org/wiki/Johnson%27s_algorithm).
He is not alone, however, in saying also that “social network analysis is an orientation towards the social world that inheres in a particular set of methods. It is not a specific body of formal or substantive social theory” (page 37).

Perhaps you are like me, and you react to this disclaimer as an example of intellectual artful dodging. Can “methods” really exist apart from ideas and assumptions—also known as “theory”—about the world around us?

Methods and theory

Not everyone writing about network analysis would agree that there is a divide between methods and theory. Stephen Borgatti, Martin Everett, and Jeffrey Johnson, major voices in this academic arena, have taken specific aim at such a claim: “some social scientists, unfamiliar with formal theorizing, have misconceived of the field as a methodology.” They acknowledge that network analysis has cultivated a distinctive mathematical methodology, but we shouldn’t let ourselves be fooled by the formality of these methods: “the theoretical concepts that are so emblematic of the field, such as centrality and structural equivalence, are just that: theoretical concepts that are part of a distinctive approach to explaining the social world” (Borgatti et al. 2013: 10).

In the next post in this series, I will begin exploring the ways in which network analysis can help us both ask and then try to answer well-formulated research questions in the social and historical sciences.

Right now, however, I only want to say that both of the examples these three co-authors offer us in this quotation—centrality and structural equivalence—strike me as far from compelling evidence that there is more to network analysis than just the analytical methods used.

However, there is an obvious question still needing an answer.

What is a network?

Just as the proof of the pudding is in the eating, so too, a definition of what something is supposed to mean is only as good as it proves useful. In a real sense, therefore, this entire series on dynamic network analysis could be seen as an extended dining experience (yes, admittedly a rather unconventional analogy). Even so, we need at least a working definition of what is a network, and I suggest this one might do at least at the start:

A network is an interrelated series of events having consequences affecting the likely repetition of those interactions.

At this stage in this series, I only want to point out a few of the implications of such a definition.

First, just as it takes two to tango, so too, it takes at least two people, things, or places to form a network, i.e., ≥N=2. As discussed previously, the events constituting a dyadic network relationship must be repetitive and not randomly so. Furthermore, what happens as part of such a relationship is dependent at least to a degree on the conditions under which the events occur. Differing situational conditions may give rise to differing interactions. Moreover, when interactions happen may be contingent on what has occurred since the last event in the relationship that has possibly changed the situation and the particulars of the interaction.

Second, while mathematicians may have fun solving abstract mathematical problems using graph theory, it is probably fair to say that many, maybe most, people doing network analysis are not doing so for abstract reasons. I am not alone in thinking that what makes network analysis worth doing is minimally the prospect that such analyses can help us pin down in real-world situations the consequences, positive or negative, of networked interactions.

Figure 1
A basic classification of networks

Therefore, as suggested in Figure 1, it can be argued that networks generally all have the three dimensions I have been labeling as situational, circumstantial, and consequential.

However, when it comes to social network analysis, we need to add the dimension of intentionality, a dimension only briefly mentioned in an earlier posting in this series. Furthermore, the intentionality of social interactions (events) between two or more individuals (network analysts seem to favor calling them agents or actors) is not limited solely to our own species. Ask any dog, cat, or wolf of your acquaintance should you have doubts that this is so.

This having been said, it is also important to recognize a distinction that can be usefully drawn between relationships that are intentional—people and other clever animals can cooperate, for instance, to get things done—and networks that are, in addition, purposeful: they are designed as networks of interactions to get things done even when the intentions of the individuals involved in such networks vary.

Perhaps one of the most exotic examples of such a purposeful network would be the ancient trade routes of the Silk Road connecting East with West.  Or its modern and sinister namesake, the black market for illicit drugs hidden on the Internet. Another shameful example would be the water supply system of the city of Flint, Michigan.

What’s next?

As I will be exploring in later posts, many analysts are chiefly interested in studying networks that have been specifically designed by those involved to accomplish such larger objectives. As the next step in this series, however, I want to ask what studying networks is good for.

“From the view of social network analysis, the social environment can be expressed as patterns or regularities in relationships among interacting units. We will refer to the presence of regular patterns in relationship as structure” (Wasserman and Faust 1994: 3).

References cited

Borgatti, Stephen P., Martin G. Everett, and Jeffrey C. Johnson (2013).  Analyzing Social Networks. Los Angeles: Sage Publications.

Knoke, David and Song Yang (2008). Social Network Analysis, 2nd ed. Los Angeles: Sage.

Scott, John (2000). Social Network Analysis: A Handbook. Los Angeles: Sage.

Wasserman, Stanley and Katherine Faust (1994). Social Network Analysis: Methods and Applications (Vol. 8). Cambridge University Press.

This is Part 6 in a series of posts introducing dynamic network analysis. Next up: 7. Why do network analysis?


© 2018 John Edward Terrell. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author(s) and source are credited. The statements and opinions expressed are those of the author(s) and do not constitute official statements or positions of the Editors and others associated with SCIENCE DIALOGUES.

Leave a Reply