The absolutely most fundamental

I recently revisited some social network classics, and this post collects random thoughts about them. In sum, I want to cheer on research on the foundations of social network theory. Not because the house would crumble without stronger foundations but because that’s where the coolest future discoveries will be. These reflections are rough, quick, and ill-researched. I’d be happy if you pointed out stuff that I missed 😊

Our pioneering papers, facing uncharted swathes of reality, needed to make assumptions to get any exploration done at all. That’s cool. But these fundamental assumptions later became truisms, and too few returned to justify them empirically. I will discuss social networks, but the same issues probably remain throughout network science [1].

In social network analysis, maybe in network science in general, the idea that network structure begets function is one such assumption. It is undoubtedly not always false, but we need to learn more about how applicable it is.

More concretely, authors usually surmise one can ignore individual traits. Personality, response time, ability to process information, propensity to spread it further, etc., are rarely investigated as confounding factors. I.e., authors assume the network positions of actors have a stronger correlation with their roles (functions) than what individual traits do. Let’s call this the doctrine of structure (short for “the doctrine of the precedence of structural explanations”).

Another tenet—sometimes overlapping with the doctrine of structure—is that social networks represent opportunities independent of time and whatever spreads on the network. E.g., in the Strength of weak ties, Granovetter assumes that the search for jobs doesn’t alter the network one uses to find jobs. We can call this doctrine of perpetuity. There are theoretical attempts to alleviate this assumption—cf., the adaptive network literature (Gross, Sayama, 2009)—but I don’t know any paper trying to assess the degree to which it is relevant.

The final basic assumption I can think of (there may be more), the doctrine of unity, is that it is meaningful to assume one underlying social network that network data are manifestations of. The literature about measurement errors (Holland, Leinhardt, 1973), informant accuracy (Wasserman, Faust, 1994, ch. 2.4.4), and the ability to understand one’s social surroundings (Freeman, Freeman, Michaelson, 1988) give many examples of this assumption. Like the other doctrines, this can neither be true nor false. But more than the others, it’s a question about what is meaningful for social theory than something we could outright validate. Of course, one can think of different types of social networks, but links of various kinds would be interdependent in complex ways—online friendships could become offline if needs be, etc.

Investigating the doctrines would be very valuable in itself, but I don’t have very concrete ideas of how to proceed. Ultimately, without Google-level data on individuals, the answers can probably not be to mine datasets aggregated for other purposes. We computational social scientists would need to collect data actively [2]. Maybe gamification could do the trick (as recently successfully done in the study of human navigation (Coutrot et al. 2022). Or clever network intervention experiments (Valente 2012). Or perhaps one could meta-analyze higher-level studies [3].

The final motivation for studying the most fundamental questions about social networks is to find catchy higher-order laws. As far as I remember, Milgram’s idea for his small-world network experiment came from Pool and Kochen’s notes—mainly abstract thoughts about the size of acquaintance circles.

Notes

[1] For metabolic networks, a similar truism is that they are modular. At the same time, they are connected into a giant component, so regarding them as modular should be seen as a working hypothesis that needs verification. But, at least when I was more active in that area, too few papers were doing that.

[2] The recent resurrection of the weak-ties problem could be an inspiration (although it is an exclusive approach since it requires collaborating with a platform like LinkedIn—Rajkumar 2022). Sagalnik, Dodds, Watts (2006) is another shining example of that type of expensive computational social science.

[3] Think of the theory that it is advantageous to have access to a greater variety of information (or material, opportunities, etc.) by virtue of being on the boundaries between social groups. There are several variants of this idea—agents in such a position have been called “gatekeepers” (Lewin, 1947), “opinion leaders” (Katz, Lazarsfeld, 1964), or “brokers” (Burt, 1992). These are not identical concepts, but all come from deductive reasoning (maybe tacitly) assuming the doctrines and that some information or opinion propagation on the network is our actual research object [4]. Probably, for some relatively general assumptions about the dynamics, the doctrines are almost equivalent to the theories named above. This means that we could, in principle, use higher-order studies to validate the more fundamental ones.

[4] Lewin studied how households obtained food, Katz & Lazarsfeld studied rumor propagation, and Burt primarily had economic transactions in mind.

References

RS Burt, 1992. Structural Holes. Cambridge, Harvard University Press.

M Granovetter, 1973. The strength of weak ties. Am. J. Sociol. 78, 1360–1380.

T Gross, H Sayama, 2009. Adaptive Networks. Springer, Berlin.

LC Freeman, SC Freeman, A Michaelson, 1988. On human social intelligence. J. Soc. Biol. Syst. 11(4), 415–425.

PW Holland, S Leinhardt, 1973. The structural implications of measurement error in sociometry. J. Math. Sociol. 3(1), 85–111.

E Katz, PF Lazarsfeld, 1964. Personal Influence. The Free Press, New York.

K Lewin, 1947. Frontiers in group dynamics. Human Relations. 1:143–153.

IS Pool, M Kochen, 1978. Contacts and influence. Social Networks 1:5–51.

K Rajkumar, G Saint-Jacques, I Bojinov, E Brynjolfsson, S Aral, 2022. A causal test of the strength of weak ties. Science, 377:1304–1310.

MJ Sagalnik, PS Dodds, DJ Watts, 2006. Experimental study of inequality and unpredictability in an artificial cultural market. Science 311:854–856.

J Travers, S Milgram, 1969. An experimental study of the small world problem. Sociometry 32, 425–443.

TW Valente, 2012. Network interventions. Science 337:49-53.

S Wasserman, K Faust, 1994. Social Network Analysis. Cambridge, Cambridge University Press.