Meeting Strangers and Friends of Friends: How Random Are Social Networks?

Abstract

We present a dynamic model of network formation where nodes find other nodes with whom to form links in two ways: some are found uniformly at random, while others are found by searching locally through the current structure of the network (e.g., meeting friends of friends). This combination of meeting processes results in a spectrum of features exhibited by large social networks, including the presence of more high- and low-degree nodes than when links are formed independently at random, having low distances between nodes in the network, and having high clustering of links on a local level. We fit the model to data from six networks and impute the relative ratio of random to network-based meetings in link formation, which turns out to vary dramatically across applications. We show that as the random/network-based meeting ratio varies, the resulting degree distributions can be ordered in the sense of stochastic dominance, which allows us to infer how the formation process affects average utility in the network. (JEL D85, Z13)

An Overview of Social Networks and Economic Applications

“…Nevertheless, social networks exhibit a full spectrum of degree distributions across different applications, ranging from one extreme where the distribution of links is nearly as if they were formed uniformly at random (e.g., matched well by distributions of romances among high school students in the Add-Health data set) and another extreme where there the distribution is nearly scale-free (e.g., the www from Albert, Jeong, and Barabasi (1999) and Huberman and Adamic (1999)). Thus, although many networks have fatter tails than one would see uniformly at random, when statistically fitting degree distributions they can come out somewhere between the extremes of a scale-free and being formed uniformly at random, as discussed by Jackson and Rogers (2007). 19,20 interview process, degree can be underestimated either by some cap imposed by the interview or the memory of the interviewee; while if degree is estimated by some computer program that "crawls" from one web page to another then it can be biased towards finding larger degree nodes.…”

“…Clustering can be traced to a variety of sources: it occurs quite naturally if friends meet new friends via their current friends (see Jackson and Rogers 2007). Institutional structures and geography can also affect who meets whom or who might benefit from interacting with whom.…”

“…Models developed by Vasquez (2003) and Jackson and Rogers (2007) span between uniformly random link formation and something like preferential attachment. The key to these models is that they have some combination of links formed uniformly at random and others that are based on existing network structure.…”

Competition and the Dynamics of Group Affiliation

“…• Groups are an important foci for the formation of new social ties between individuals [39]; however, social ties may also form between 'strangers' [20].…”

Using Affiliation Networks to Study the Determinants of Multilateral Research Cooperation: Some Empirical Evidence from EU Framework Programs in Biotechnology

“…On the one hand, social proximity might be a relevant dimension in the sense that a consortium is not merely a medium for knowledge production but also a medium for social interaction. Social ties can play a role to convey information on possible consortiums, their compositions; and make it easier to identify cooperation alternatives and get into contact with them as shown theoretically and empirically in other contexts (Jackson and Rogers, 2007;Fafchamps et. al.…”