social networks ARE different


A while ago, I complained about the trend among natural scientists who study networks to write papers suggesting vague general laws that subsume social, neural, metabolic, web, power-plant, and you-name-it, “networks.” The standard mode of writing this paper is to take some sort of network, compute some graph statistics (degree distribution, mean path-length, clustering coefficients, etc.) and suggest that the observed properties are “similar” to those observed in other networks, which points to some sort of fundamental set of laws that govern all networks.

This Fleckian thought-style, I suggested is what has made Physics very succesful, but it is of little pragmatic use to sociologists. We are interested in what makes social networks different from other networks. We are not interested in finding any network theory of everything that can be written down into an equation that fits in your workout t-shirt.

It turns out that all my complaining and moaning was for naught. Mark Newman (who I got to see at a talk given to Barabasi’s seminar here in South Bend last semester), one of the few physicists who is actually familiar with the sociological literature (he hung out at Santa Fe and is now at Center for the Study of Complex Systems at Michigan, one of the few places where interdisciplinary research in the social sciences is alive and well) had already written a 2003 Physical Review E (E is for excellent) paper precisely designed to address my afore-mentioned worries. In the paper Newman and Park address an interesting question, namely the reasons why not all networks are the same, and in particular the issue of why social networks are systematically different from non-social networks.

The two major differences are: (1) in social networks the degree (number of links, friends, advisers, etc.) of adjacent vertices are positively correlated; in non-social networks (i.e. the web, food chains, etc.) they are negatively correlated and (2) social networks exhibit inordinately high degrees of clustering (relative rarity of the “forbidden triad”) a fact that is simply not observed in non-social networks.

Newman and Park argue that the fact that social networks tend to partition themselves into communities (Simmelian groups) has a lot to do with both of these unique properties. They surmise that the observed degree correlation and clustering of the network can be recovered by postulating a community model, basically a two-mode bipartite graph in which individuals are assumed to belong to groups of different size and to be indirectly connected to one another, raising the probability of a direct connection, through such groups. Groups create positive degree correlation through their differential size distribution (individual in small groups will be more likely to be tied to other individuals in the same small group and vice versa).

This is consistent with early sociological network theory (Breiger 1974; Feld 1981) that spoke of the dual constitution of persons and groups and how groups served as “social foci” that structured dyadic interaction in predictable ways. Although not all of the tendency for positive degree correlation and clustering can be explained by a simple community model, the fact that human networks are structured by larger corporate entities goes a long way to explaining how social agents are different from dumb power plants.

Written by Omar

April 4, 2007 at 2:10 pm

Posted in networks, omar

2 Responses

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  1. In the same year, he also published this:



    April 4, 2007 at 3:47 pm

  2. […] are a few old posts by Omar (here, here, and here) about the “new science” of […]


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