Dynamic Network Analysis 6. What is a network?

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.

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.

Figure 1
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 of a continuing series of posts on dynamic network analysis. 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.

Dynamic Network Analysis 5. What’s a relationship?

NOAA's National Weather Service (NWS) Collection. Location: Orange, Australia. Photographer: Mr. Shane Lear (image wea00628);

John Terrell

DEFINITIONS OF WHAT IS A NETWORK differ in their wording and focus, but a common theme is that different types of relationships give rise to different types of networks.

So if we measure friendship ties, we have a friendship network, and if we also measure kinship ties among the same people, we have both a friendship network and a kinship network . In the analysis we may choose to combine the networks in various ways, but in reality we have two networks. (Borgatti et al. 2013: 3)

In response to such a statement, all I can say is “Oh, really?” The assumptions embedded in these seemingly straightforward words are fairly typical of how network analysis is commonly defined by experts as a way to study the world and our place in it. They are all questionable.

An example of a social network diagram. By Wykis [Public domain], from Wikimedia Commons
What, for example, is “friendship” (Terrell 2014)? Is it even possible to have a single and consistent right answer to such a question so that every friendship included in a network of friendships is predicated on the same or at least comparable human feelings, commitments, and acts? Additionally,  as social anthropologists know well after many decades of study and debate, don’t even try to see “kinship” as a universally consistent type of human social engagement.

What is a relationship?

Let’s reflect a moment on what I just wrote. Except as an academic exercise, does anyone honestly believe the nuanced relationships that humans have with one another can be usefully seen as a layering of separate networks? So much so, that all of the networks included in any given social network analysis are somehow layered together in a fashion that might be described as some sort of “social sandwich”—to offer an admittedly peculiar simile?

You can probably tell without my having to say so that I want to offer you another way to think about networks and doing network analysis.

Networks are a way of thinking about social systems that focus our attention on the relationships among the entities that make up the system, which we call actors and nodes (Borgatti et al. 2013: 1)

Instead of seeing networks the way most analysts do as systems (Kolaczyk 2009: 2) or structures (Scott 2000: 4), I will show you how it is useful as well as more truthful to describe dynamic network analysis athe study of related events in time and space of differing and variable probability. Importantly, whether the events being analyzed are predictable enough to characterize their co-occurrence as a “system” or “structure” is a matter to be investigated as part of any dynamic network analysis, not something to be assumed at the beginning of study.

Before exploring all this with you, however, I first need to tell you what I mean by the word relationship.

Begin at the beginning
By Sidney Paget (1860-1908) (Strand Magazine). Public domain, via Wikimedia Commons

Let’s take things one step at a time. Let’s begin by revisiting what Carlo Rovelli has told us about electrons that got him into trouble with Lisa Randall:

 Electrons don’t always exist. They exist when they interact. They materialize in a place when they collide with something else. The “quantum leaps” from one orbit to another constitute their way of being real: an electron is a combination of leaps from one interaction to another.

Lightning fill in the blank

I don’t think it would be stretching the point too far to say lightning can be said to exist or not exist in a similar way. As helpfully described by the National Severe Storms Laboratory:

Lightning is a giant spark of electricity in the atmosphere between clouds, the air, or the ground. In the early stages of development, air acts as an insulator between the positive and negative charges in the cloud and between the cloud and the ground. When the opposite charges build up enough, this insulating capacity of the air breaks down and there is a rapid discharge of electricity that we know as lightning. The flash of lightning temporarily equalizes the charged regions in the atmosphere until the opposite charges build up again.

To the human observer, the potential for a bolt of lightning to occur is only something suspected, something lurking in the background, so to speak,  before the actual discharge. But the discharge finally neutralizing the imbalance in positive and negative charges that has been developing on the sly doesn’t take place until the relationship between the positive and negative sides of the imbalance finally materializes with what can often be a spectacular display of nature’s given ways.

The famous opening words of a novel by Edward Bulwer-Lytton published in 1830 that are now notorious as an example of purple prose (i.e., overly melodramatic writing). https://www.smith.edu/libraries/libs/rarebook/exhibitions/dickens/16-paul-clifford.htm

Yet the potential for such a dramatic and utterly natural demonstration of light, sound, and at times destructive effect had been there long before this event takes place.

This simple fact raises a basic question. If lightning  is the consequence of a growing imbalance between positive and negative electrical charges, say, on “a  dark and stormy night,” then what makes this kind of dyadic relationship in nature different from the sorts of relationships that can develop between friends, colleagues, and loved-ones? And what does all this have to do with network analysis?


Repeat after me

Despite the old saying, it is a well-known fact that lightning can strike the same place more than once. As one storm enthusiast on the Internet has  commented, given enough time, this outcome is actually inevitable. He adds, however—and more to the point I want to make in case you are wondering why on earth I am still talking about lightning—the electrical activity in the storm that produced it may generate another strike as soon as as the imbalance has again grown strong enough. Once this happens, a previously hit location again becomes fair game as a recipient of the next discharge. If this weren’t so, there would be no practical need for installing lightning rods on tall buildings and such like.

Being fair game in a relationship is hardly grounds for claiming as well that the cloud in question has formed some kind of a relationship with the location previously hit. Nor is there any sure way to predict whether the same cloud will strike the same place.  Maybe another cloud that same day or sometime in the near or distant future may also strike the same place. But there is no guarantee when, and there will be absolutely no  connection—no relationship—between the first responsible storm and the later culprit cloud involved.

So here then is one critical difference between the kind of patterned and (seemingly) repetitive type of dyadic event in nature called a lightning strike and the kind of patterned dyadic relationship that occurs in networks of many types, human and otherwise: a network relationship however materialized is not just dyadic but also repetitive.

Relational data . . . are the contacts, ties and connections, the group attachments and meetings, which relate one agent to another and so cannot be reduced to the properties of the individual agents themselves. Relations are not the properties of agents, but of systems of agents; these relations connect pairs of agents into larger relational systems. (Scott 2000: 3)
What else is involved?

What else does it take to turn a repetitive dyadic relationship between two things, people, or places into a broader network relationship? The easy answer would that there is a lot that can come into play. However, there are at least three critical elements in addition to the requirement that the relationship needs to be repetitive and more than just randomly so. What are they? I like to label them as situational (or circumstantial), contingent, and consequential.  Let’s consider each in turn starting with the first.

SituationalIt is conventionally said in text books about network analysis that there are two basic kinds of data about this world of ours, attribute data and relational data. The former is said to be information about the properties, qualities, or characteristics of the two entities ( for example, the individuals or groups involved) in the dyadic relationship being analyzed—classically, the sorts of information that can be quantified, classified, and analyzed using the many statistical tests of significance that have long been available and are nowadays fairly easy to run on most computers.


Relational data, on the other hand, is information about the linkages, contacts,  and connections (called “edges” or “ties” in network analysis) among the entities (called “nodes” or “vertices”) being studied. All well and good, but as we will be discussing in this blog series, when the entities in particular are individuals and groups of people, for instance, the characteristics of interest in any given study often vary depending on the particulars of the situation—the context—they are dealing with. The relationship between Rapunzel and the prince who courted her in the famous fairy tale, for instance, is situationally quite different from what most lovers must deal with to be with one another.

Contingent—Similarly, when and perhaps even whether a relationship is maintained over the course of time may often be contingent, or dependent, on the situation at any given moment on either, or both, sides of the relationship. For instance, whether you flee from what has been your home and seek refuge elsewhere when faced with an environmental disaster or political turmoil may be contingent on whether you have reason to believe there is someone who will be there at the end of your journey who will take you in and help you survive.

A Yemenite family walking through the desert to a reception camp near Aden, 1 November 1949. [Public domain], via Wikimedia Commons] Part of the Jewish exodus from Arab and Muslim countries. “Between June 1949 and September 1950, the overwhelming majority of Yemen’s Jewish population was transported to Israel in Operation Magic Carpet. After several waves of persecution throughout Yemen, most Yemenite Jews now live in Israel, while small communities are found in the United States and elsewhere. Only a handful remain in Yemen.” https://en.wikipedia.org/wiki/Yemenite_Jews

ConsequentialThirdly, relationships may be as seemingly trivial as saying good morning to your neighbor when you go outside to pick up your  morning newspaper, but network analysis is a way of pinning down and understanding how relationships can have consequences of real significance, even in instances such as remembering to say hello to a neighbor that most times may seem inconsequential, but not always. It not only takes a community to raise a child, but being on good terms with your neighbors can be highly consequential, for example, when you need to raise a new barn, say, to replace one that burned to the ground after it was struck by lightning. 

Barn raising – Leckie’s barn completed in frame. By John Boyd (Public domain) via Wikimedia Commons
What about intentional relationships?
Alice in Wonderland by George Dunlop Leslie (1835-1921).  Public domain, via Wikimedia Commons

When it comes to the analysis of human relationships, there is no doubt whatsoever that more needs to be considered than just the four relational dimensions noted so far: repetitive, situational, contingent, and consequential. 

The relationship between a parent and child, for instance, not only exhibits all four of these characteristics, but is also a motivated or intentional relationship, for better or for worse. Moreover, we humans are not the only creatures on Earth capable of forming and maintaining intentional relationships, as anyone who has ever worked with dogs knows well.

Clearly, therefore, there is more to be said about what is a relationship. However, it is now time to begin asking a similarly basic question. What is a network of relationships?

This is the topic of my next blog in this continuing series on dynamic network analysis.

The Wilderness Hunter: An account of the big game of the United States and its chase with horse, hound and rifle, by Theodore Roosevelt (1903). By Internet Archive Book Images (No restrictions), via Wikimedia Commons

References cited

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

Kolaczyk, Eric D. (2009). Statistical Analysis of Network Data: Methods and Models. New York: Springer.

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

Terrell, John Edward (2014). A Talent for Friendship: Rediscovery of a Remarkable Trait. New York: Oxford.

  • This is Part 5 of a continuing series of posts on dynamic network analysis. 6. What is a network?
    © 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.

COMING SOON Commercial DNA testing and those pesky “ethnicity estimates.”

John Terrell

060628-N-6645H-025  U.S. Navy photo by PhotographerÕs Mate 3rd Class Adam Herrada (RELEASED)

AFTER YOU HAVE SENT to them a carefully collected sample of your spit or a used buccal swab along with your PayPal information, commercial DNA testing companies are likely to send back to you what they have found therein reported as your very own personal “ethnicity estimates“—usually expressed as percentages of this-and-that such as 43% West European, 18% Scandinavian, 6% Irish/Scottish/Welsh, 3% Finnish/ Russian, etc. all adding up to 100%.

If you go online to find out what on earth these percentages are telling you (for example, here) you are likely to get a great deal of misinformation.

Stay tuned to SCIENCE DIALOGUES for a penetrating critique of these pesky little percentages and the less than wonderful racial assumptions lurking within them.