Dynamic Network Analysis: 8. Adaptive networks

If you want to learn not just how social relations are structured but also why, then it would be naive to assume what you are seeing can be explained solely by social properties and processes.

Mount Stuart Royal Naval Hospital, 1914-1919 Wellcome V0029750.jpg (https://creativecommons.org/licenses/by/4.0)], via Wikimedia Commons

John Terrell

WHAT CAN NETWORK ANALYSIS ACCOMPLISH beyond data mining, mapping, and fancy (or plain) visualization? Not an easy question to answer. The published literature on networks is enormous. I am going to focus now, therefore, only on social network analysis with the understanding that later I will have things to say, as well, about other applications.

If all you have is a hammer

Consider the popular expression often attributed (wrongly, it seems) to Mark Twain: “if all you have is a hammer, everything looks like a nail.” Having recently surveyed the last ten years of research papers published in the journal Social Networks, I think it is possible to say a few things in general about the state of this research pursuit. While there are numerous exceptions, of course, many doing social network analysis seem so committed to the established structuralist view of networks that this saying might just as well be rephrased as “if all you have is a network, everything looks like a structure.” Since what I mean by saying this is probably far from clear, here’s the issue I have with this narrowly focused sociological take on network analysis.

There are only so many ways a given number of things (call them N) can be connected together, mathematically speaking. For example, the maximum number of simple ties among N=10 things is N(N-1)/2, i.e., 45. Therefore, even if we must know for some excellent reason how N=10 things are linked (that is, “structured”) in ways equal to or less than this maximum number of ties, surely this cannot be all we need to know to understand why these ten things are structurally connected with one another in one way or another.

Yet what I have taken away from reviewing the past ten years of research papers in Social Networks is that the focus of much of the work being reported is often more about methodology—the “hammer,” so to speak—than about what to build with it worth the investment of time, money, and effort.

A limited tool kit

Here’s another way of saying what I just said. While going through articles in this journal I was repeatedly surprised that network analysis seems to be used only rarely to model and test explanatory research hypotheses. Instead, even when real-world data are included as part of the exercise, what is often invoked are a small number of social network’s own proprietary  analytical concepts labeled as “parameters” and “social processes” used in ways which are not only descriptive but often also seemingly explanatory (e.g., Fitzhugh and Butts 2018). Typical examples are these: centrality, densitytransitivity, clustering, reachability, and so forth (Hanneman and Riddle 2005). I won’t try to explain here what these are, but include links that describe them in some detail.

I find it is hard to know what to make of these so-called parameters and processes. For instance, here is what one well-known online handbook  tells us about the sociological concept of power: “All sociologists would agree that power is a fundamental property of social structures. There is much less agreement about what power is, and how we can describe and analyze its causes and consequences.” Following this candid but confusing observation, we are then told:

Network thinking has contributed a number of important insights about social power. Perhaps most importantly, the network approach emphasizes that power is inherently relational. An individual does not have power in the abstract, they have power because they can dominate others—ego’s power is alter’s dependence.

What I want to underscore about this assertion is that apparently such an observation is not being offered to us as a research hypothesis suitable for testing against data. Instead, we are evidently being asked to accept this portrayal of power, whatever you take it to be, as a statement of truth.

Why do network analysis?

The passages quoted above come from a standard and extremely helpful introduction to social network methods by Robert Hanneman and Mark Riddle published back in 2005. This guide for the perplexed is still freely available on the Internet today. These authors are careful to tell us what they see as the three main reasons for using the methods they describe.  Here they are, rewritten to abbreviate them:

  1. The matrices and graphs at the heart of network analysis are compact and systematic ways to manage information and manipulate data efficiently so we can detect structural patterns that otherwise can be tedious to document and hard to see;
  2. since these methods are quantitative and mathematical, we are able to use computers to analyze networks data, even massive amounts of it; and
  3. these rules and methodological conventions can help us do more than communicate effectively; they can also help us discover things in our data we might not even think to look for using only words to describe and summarize the relationships reflected in the information we have.

You may disagree, but I think these three strengths are basically those I have previously labeled as mining, mapping, and visualization, although I haven’t yet mentioned using computers.

In any case, I am certainly not alone in thinking there is more to social network analysis than just these three strengths. As these authors themselves say in the afterword that concludes their handbook:

The basic methods of studying patterns of social relations that have been developed in the field of social network analysis provide ways of rigorously approaching many classic problems in the social sciences.  The application of existing methods to a wider range of social science problems, and the development of new methods to address additional issues in the social sciences are “cutting edge” in most social science disciplines.

Unfortunately, they say nothing at all about what these problems and additional issues may be. Their closing words are simply these:

we have not touched on very much of the substance of the field of social networks—only the methodologies. Methods are only tools. The goal here is using the tools as ways of developing understanding of structures of social relations. The most obvious next step is to read further on how network analysis has informed the research in your specific field. And, now that you are more familiar with the methods, you may see the problems and possibilities of your substantive field in new ways.

Integrative networks

Despite these inconclusive words at the end of this influential handbook, social network analysis has never been solely about mathematical methods and formal procedures. In 2012, for example, an issue of Social Networks was entirely devoted to exploring the common ground between social network research and geographic spatial analysis even though it was acknowledged that “the formal integration of social network and spatial analytic strategies remains relatively  underdeveloped in the literature” (Adams et al. 2012: 1).

Although there have been advances since then such as the use of adaptive network modeling in restoration ecology (Raimundo et al. 2018) and in understanding how violent crime effects inter-neighborhood community patterns in Chicago (Graif et al. 2017), this goal still seems a long way off.

Does this matter? Perhaps not if all that you want to do is map and visualize the relationships among N things, people, or places to offer plausible interpretations of the observed structural arrangements, but is this the most that network analysis can hope to achieve (Doreian and Conti 2012)?

Over forty years ago (Terrell  1977), I suggested that similarities and differences among local human populations reflect the workings of an integrated complex of variables and relationships that can be idealized as a geographic system (Figure 1).

Figure 1. “The concept of geographic systems can be described using an elementary model to depict how local populations and the habitats they occupy may all be seen as interrelated within a comprehensive network of interactions. The concept itself may be defined as follows: a geographic system is the interactive configuration among the size, distribution and interaction structure of a set of local populations and the elements and interaction structure of the area of their occurrence, analysed as a complex of intercommunicating variables within which a change in any one variable or relationship is likely to effect changes, of a greater or lesser degree, in all the others. It probably is not necessary to add that such a complex of variables and relationships is unlikely to respond only to single causes, although changes in some dimensions may be more influential on the system as a whole than changes in others” (Terrell 1977: 65).

Back then I knew that from this integrative perspective it wouldn’t do to reply on categorical units labeled for convenience as “populations,” “habitats,” “geographic regions,” and the like. At this same time, therefore, I began to explore using network approaches inspired by work in locational geography (Terrell 1976). As shocking as it may seem to network sociologists, I knew absolutely nothing at that time about the work of Harrison White, one of the founders of the modern sociological networks tradition, even though I had been an undergraduate and later a graduate student at Harvard. The distance between Anthropology and Sociology there in Cambridge, Massachusetts, back then was not geographic but social and cultural.

I was also inspired by ecology and biogeography as practiced then. But here, too, I saw one had to be careful not to borrow from other disciplines without being watchful. As I wrote in 1977:

the geographic system concept resembles that of an ecosystem and encompasses the trophic or food relations between man and his environment which are specifically explored by human ecologists. The concept, nevertheless, is intended to be more inclusive than that of an ecosystem, in order to avoid the a priori assumption that an analysis of the interactions within and among human populations can be reduced to a study of the trophic, biochemical and species structures of their environment and the functioning of those structures. (Terrell 1977: 65).

While I won’t try to detail the reasons, I was also dissatisfied with the idea that the Earth can be subdivided into geographic regions, and with the convention back then that networks are systems (nowadays I would be more vocal about saying that systems are networks, but not all networks are systems).

A geographic system . . . is a set of biological and ecological elements, their structural relationships, and their functional operation. . . . [W]hile geographic regions have spatial boundaries by definition,  geographic systems do not. All the communities living within a region may be usefully called a regional population, yet it is conceivable and even likely that a given region, defined spatially, may house two or more fairly distinct “system populations” which interact little if at all among each other.

Even thus qualified, I felt more needed to be said, and followed these observations with words of caution. “The world in all its complexity is not, after all, a mosaic of discrete parts or ‘regions'” (Terrell 1977: 66).

Dynamic networks

Given the hindsight of 40+ years, I would now visualize what I was trying to say differently (Figure 2). Had it also been a low-cost publishing option back then, I undoubtedly would have opted to use color, not that doing so makes much difference except possibly in the visual appeal of the model:

Figure 2

What either version of this conceptual model hopefully conveys is that while one could be committed professionally to researching just a single relational dimension in this complex of relationships—as it seems most doing social network analysis today prefer to do—if you want to learn not just how social relations are structured but also why, then it would be naive to assume what you are observing can be explained solely by social properties and processes.

I have argued previously that something can be called a “relationship” if what you have in mind is repetitive, situational, contingent, and consequential. Additionally, I have also noted that two  other dimensions  need to be added when the relationships are social: intentional and purposeful.

But this is not all. Without any explanation I added earlier that another dimension needs to be included: adaptation (Figure 3).

Figure 3

I will have much to say about adaptive networks in future posts in this series. At this point, since this one is longer than I like already, let me just give you  a simple example of what I have in mind.

From a sociological perspective, what happens in a hospital operating room is unquestionably an example of a small functioning social network. Ignoring the role of the patient on the table for a moment, everyone in the room has a role to play and is related to everyone else in clearly defined ways (much more clearly defined, by the way, than would be normal outside the medical and legal environment of the operating theater).

It seems reasonable that if one wanted to, many of the standard parameters and social processes favored in sociological network analysis can be employed to mine, map, and visualize what is going on over the supine (or prone) figure lying on the operating table. But if one then stopped paying attention to the work being done, what would be the point of even just being there to witness the operation?

What would soon become painfully apparent if you stayed around longer is that as the surgical team proceeds with the operation at hand not merely  because they want to (what they are doing, in other words, is obviously intentional), but also because they hope to achieve a particular outcome (the operation is, after all, purposeful), who does what, why, when, how, and even whether evolves dynamically to meet the changing contingencies of what they come across once the patient is anesthetized, opened up, and the work begins in earnest.

What’s next

What is happening in this hypothetical operating theater is a simple example of what I want to talk about in future posts in this series when I am exploring with you not just how but also why it is good to study networks of human engagement between things, places, and people as dynamic, adaptive, evolving strategies—not just structures—for survival.

References cited
This is Part 8 of a series of posts introducing dynamic network analysis. Next up: 9. Asking questions.


© 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.

Oldest piece of cheese?

John Terrell

Recently many news outlets around the world carried the startling news that archaeologists had found the world’s oldest bread—as witnessed by this headline for a story by Helen Briggs published on 17 July 2018 in the  BBC News:

Prehistoric bake-off: Scientists discover oldest evidence of bread

NPR carried a similar story by Lina Zeldovich on July 24th:

14,000-Year-Old Piece Of Bread Rewrites The History Of Baking And Farming

These stories brought to mind a spoof I had written back in the mid 1960s  when I was in graduate school studying anthropology. I won’t discuss my motivation, but some may pick up on what was the source of my inspiration.

© 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: 7. Why do network analysis?

When you are asking good questions and trying to use network analysis to answer them, the focus should not only be on nodes and linkages, but also on exploring the consequences of the relationships being examined.

John Terrell

IT SEEMS LIKELY MANY TODAY on hearing the word “network” may assume you must be talking about an Internet outage or service delay. It seems less likely they will think you are referring to something as rarefied as network analysis.

However, people devoted to using social media in creative ways, and those paying attention to the news each day, may have at least a beginner’s understanding of the currently popular uses of this technical approach to the mysteries of the universe. Even they, however, may be minimally aware of the weaknesses, the limitations, of such research.

Furthermore, should some inquisitive souls venture as far as reading a textbook on this topic, they may decide that such books, undoubtedly impressive for their mathematics and node-link diagrams, are more about “how to” than about “why?” or “so what?”

Therefore, what are some of the demonstrated strengths of network research? What currently are some of the known weaknesses? Is there anything that can be done to overcome the latter?

Said more simply, why do network analysis?

Data mapping and visualization

Graph representing the metadata of thousands of archive documents, documenting the social network of hundreds of League of Nations personnel. (By Martin Grandjean [CC BY-SA 3.0 , via Wikimedia Commons.)
Network diagrams can be visually striking, even intimidating. Come across one or two of these visualizations in a research article, and even if you don’t know all that much about the science involved, it’s hard not to be impressed.

While granting, therefore, that network diagrams can be both pretty and impressive, evidently little is yet known about how successfully people are able to interpret such visualizations. Nor it it clear whether or when network visualizations actually improve human understanding and problem-solving. There is, however, some evidence suggesting that both data tables and network visualization are more effective ways of communicating information and scientific findings than conventional text descriptions (Welles and Xu 2018).

“The change of community structure after applying the schneider’s method [23] on the dolphin network. Fig. 1(a) presents the community structure of the dolphin network with N = 62 dolphins and M = 159 co-appearance of them. The network can be divided into 5 communities, which are marked as different colors. Fig. 1(b) presents the onion-like structure of the improved network. The community structure of the network is greatly changed. Fig. 1(c) shows the clear community structure of Fig. 1(B), i.e. the improved network. The first two figures are drawn by the Gephi automatically, while the vertices in the last figure are separated by the colors manually. The social network of 62 bottlenose dolphins was observed by Lusseau [30]. The dolphins lived in Doubtful Sound, New Zealand. Lusseau collected the data of dolphins according to his field studies of dolphins for two years. The ties between dolphin pairs are established by the observation of the statistically significant frequent association.”(Yang et al. 2015)
Data mining

Anyone shopping nowadays online at companies like Amazon have firsthand experience with the ability these firms now have using relational algorithms to track you, your tastes, where you have been on the Internet, and your prior purchases. What am I referring to? The enterprising phrase  “customers who bought this also bought” that is now standard & usual at commercial websites.

Mining what is popularly called “big data” culled off the Internet in this fashion to find correlations and patterns of association is proof enough that relational thinking can have highly profitable payoffs—even when the final product is not an attractive network visualization but instead an enticing and strongly personalized buying recommendation.

If relational data mining like this sounds more than a just little creepy to you, fair enough. The self-serving, some would say malicious, misuse of personal information mined from 87 million Facebook accounts by a company called Cambridge Analytica during the 2016 presidential election in the United States should be more than enough to convince even the most hardened skeptics that data mining using network algorithms can be more than a trivial pursuit.

“Social media analytics is the process of gathering data from stakeholder conversations on digital media and processing into structured insights leading to more information-driven business decisions and increased customer centrality for brands and businesses” (http://www.wikiwand.com/en/Social_media_analytics).
Correlation or cause?

While some purists debate whether statistically speaking “an association” is or isn’t the same thing as “a correlation,” one of the fundamental clichés of statistics is the quip that “a correlation [or association] is not a cause.” The logic behind this observation is straightforward.  Saying something (call it A) is correlated with something else (B) just means:  if A, then also B with some likelihood or degree of probability. For example: if you like A enough to buy it, then you may also want to purchase B, which the analysis of large amounts of buying data has revealed is something often also bought with it.

Correlations are rarely absolute or perfect. Even when Amazon or some other company lets you know other people who bought this also bought that, buying the latter may be something you’d never ever dream of doing. But given how often Amazon knows for sure that other people have also bought B, it is not unreasonable to think you might be willing to do so, too.

Note, however, that nowhere in the logic of “if A, then B” is it stated why  the two are likely to be purchased together. Obviously if Amazon also knew what causes the pairing of A and B,” the odds of getting someone to buy both might be greatly improved.

In any case, the lesson for us remains unchanged. Just because A and B are correlated doesn’t mean we know why or how they are. Nor do we even know when they are likely to be.

Yes, often comparison of A and B can suggest possible reasons. Both may be similar in character or for a similar purpose. For example, A is a window air conditioner, and B is a steel support bracket for this type of air conditioner. Or A is a book about sexual behavior, and B is something risqué from Victoria’s Secret. Yet while similarity may often be a useful clue, similarity and cause are not one and the same thing.

Constraints and opportunities

Although perhaps not always obvious, a correlation is a kind of pattern. Hence data mining, mapping, and visualization are ways of finding and illustrating not just dyadic correlations between A and B, but also more complex forms of relational patterning within samples of information about this, that, or something else (commonly referred to as data sets). On the face of it, therefore, if it is true that a correlation is not a cause, then so too, it should be true that a pattern is not a cause.

Or maybe complex patterns can be, at least sometimes? It is conventional to say that the goal of networks research is to learn how the patterning of ties within social networks—in the jargon commonly used, the structure of such networks—shapes human behavior (Scott 2000: 19).

Given the familiar old saying “it’s not what you know, it’s who you know,” this possibility may hardly seem worth mentioning. Doesn’t everybody know that the patterning of their relationships with others can often make or break the best-laid schemes o’ mice an’ men? Or as Stephen Borgatti and his colleagues recently expressed what would appear to be this sentiment in a less poetic way:

a generic hypothesis of network theory is that an actor’s position in a network determines in part the constraints and opportunities that he or she will encounter, and therefore identifying that position is important for predicting actor outcomes such as performance, behavior or beliefs. (Borgatti et al. 2013: 1)

If we grant at least for now that the patterning of social ties within a social network can “in part” (as these authors say) determine constraints and opportunities, then doesn’t this mean that network structure can be causal, at least some of the time? If so, then is proving this exception to the general rule that a correlation (or pattern) is not a cause more than adequate justification for pursuing networks research? Or is this justification for this kind of research making too much out of too little?

You guessed it. The question I just asked was a leading question. Surely there must be more to be gained by doing network analysis than just proving over and over again that one’s success depends on who you know, not what you know. Or maybe not?

Limiting assumptions

For me, one of the surprising limitations of many published applications of social network analysis is the evident focus not on what, when, and why the individuals or groups being studied do what they do in their actual relationships with one another, but instead on what Stanley Wasserman and Katherine Faust (1994: 8) have described as “the characteristics of the network as a whole.” Or as they have also phrased this notion: “To a large extent, the power of network analysis lies in the ability to model the relationships among systems of actors” (1994: 19).

Their commitment to such a research agenda is shared by many others doing social network analysis (Knox et al. 2006). In practice, such an agenda leads one to define the “unit of analysis” not simply as people and their relationships with one another, but instead as that vague collective something popularly called the “group”—which Wasserman and Faust are willing to define for us as “the collection of all actors on which ties are to be measured” (1994: 19).

Such a definition of what social network analysis focuses on might be more understandable if they just came out and told us that the word “group” simply means what statisticians label as a “sample.” But evidently this is not what Wasserman and Faust (and others doing network analysis) have in mind. When they write about “systems of actors,” what they want us to take these words to mean is something far more categorical:

A system consists of ties among members of some (more or less bounded) group. The notion of the group has been given a wide range of definitions by social scientists. For our purposes, a group  is the collection of all actors on which ties are to be measured. One must be able to argue on theoretical, empirical, or conceptual criteria that the actors in the group belong together in a more or less bounded set. Indeed, once one decides to gather data on a group, a more concrete meaning of the term is necessary. (Wasserman and Faust 1994: 19)

These authors do go on to tell us that dealing with such groups presents social scientists with “some of the more problematic issues in network analysis, including the specification of network boundaries, sampling, and the definition of group” (1994: 19–20). But here’s the big question. If you want to do network analysis, is it necessary to focus on groups? Why can’t the focus be on nodes and linkages? And on causes and consequences more telling, more interesting, and perhaps more mysterious than just what can be made of who we know?

What’s next?

I am hoping you agree with me that I haven’t as yet put our collective finger on why doing network analysis is a good thing to do. I will offer you in the next post in this series the basics of what I see as a better reason. Before going on to do so, however, I want to plant two thoughts in your mind.

First, it’s a big mistake to believe that network analysis has to be about studying something called “the whole network.” Given even the most basic math (N=2n), it is obvious that as the number of nodes increases, the complexity of “the whole” can grow so swiftly that practically speaking, the best any one can do is study samples, not groups or wholes however defined.

Second, if you are really interested in asking good questions and trying to use network analysis to help you try to answer them, then not only should the focus be on nodes and linkages “down on the ground,” so to speak. But also on exploring the consequences of the relationships, human or otherwise, under observation.

In particular, as I will discuss in the next post, we need to add to our classification of networks another column and label it “adaptive.”

References cited

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

Knox, Hannah, Mike Savage, and Penny Harvey (2006). Social networks and the study of relations: Networks as method, metaphor and form. Economy and Society 35: 113–140.

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.

Welles, Brooke Foucault, and Weiai Xu (2018). Network visualization and problem-solving support: A cognitive fit study. Social Networks 54: 162–167.

Yang, Yang, Zhoujun Li, Yan Chen, Xiaoming Zhang, and Senzhang Wang (2015). Improving the robustness of complex networks with preserving community structure. PloS one 10, no. 2 : e0116551.

This is Part 7 in a series of posts introducing dynamic network analysis. Next up: 8. Adaptive networks.


© 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: 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.

Dynamic Network Analysis: 5. What is a relationship?

Instead of seeing networks as systems or structures, it is useful as well as more truthful to describe dynamic network analysis as the study of relational events in time and space of differing character and probability.

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 (DYNA) athe study of relational events in time and space of differing character and 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 in a series of posts introducing dynamic network analysis. Next up: 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.