Stochastic network formation and homophily

This is a chapter of the forthcoming Oxford Handbook on the Economics of Networks

Tributes & Remembrances

From a memorial service held in memory of Charles Price, Professor Emeritus of Art History, at Harkness Chapel, Connecticut College, April 13, 2004. With tributes written by Barbara Zabel, Christopher London, Brian Rogers, Cynthia Willauer, Maureen McCabe and John H. B. Knowlton. Illustrations by Charles Price

Diversity and Popularity in Social Networks

Homophily, the tendency of linked agents to have similar characteristics, is an important feature of social networks. We present a new model of network formation that allows the linking process to depend on individuals types and study the impact of such a bias on the network structure. Our main results fall into three categories: (i) we compare the distributions of intra- and inter-group links in terms of stochastic dominance, (ii) we show how, at the group level, homophily depends on the groups size and the details of the formation process, and (iii) we understand precisely the determinants of local homophily at the individual level. Especially, we find that popular individuals have more diverse networks. Our results are supported empirically in the AddHealth data looking at networks of social connections between boys and girls.Social networks, Network formation, Homophily, Diversity

Diversity and Popularity in Social Networks

Homophily, the tendency of linked agents to have similar characteristics, is an im- portant feature of social networks. We present a new model of network formation that allows the linking process to depend on individuals types and study the impact of such a bias on the network structure. Our main results fall into three categories: (i) we compare the distributions of intra- and inter-group links in terms of stochastic dominance, (ii) we show how, at the group level, homophily depends on the groups size and the details of the formation process, and (iii) we understand precisely the determinants of local homophily at the individual level. Especially, we ¯nd that popular individuals have more diverse networks. Our results are supported empirically in the AddHealth data looking at networks of social connections between boys and girls.social networks, homophily, AddHealth, diversity, degree distributions

The Economics of Small Worlds

We examine a simple economic model of network formation where agents benefit from indirect relationships. We show that small-world features—short path lengths between nodes together with highly clustered link structures—necessarily emerge for a wide set of parameters

The Economics of Small Worlds

We examine a simple economic model of network formation where agents benefit from indirect relationships. We show that small-world features - -- short path lengths between nodes together with highly clustered link structures --- necessarily emerge for a wide set of parameters.networks, small worlds

Homophily and Long-Run Integration in Social Networks

We model network formation when heterogeneous nodes enter sequentially and form connections through both random meetings and network-based search, but with type-dependent biases. We show that there is "long-run integration," whereby the composition of types in sufficiently old nodes' neighborhoods approaches the global type distribution, provided that the network-based search is unbiased. However, younger nodes' connections still reflect the biased meetings process. We derive the type-based degree distributions and group-level homophily patterns when there are two types and location-based biases. Finally, we illustrate aspects of the model with an empirical application to data on citations in physics journals.Comment: 39 pages, 2 figure

Strategic Immunization and Group Structure

We consider the spread of a harmful state through a population divided into two groups. Interaction patterns capture the full spectrum of assortativity possibilities. We show that a central planner who aims for eradication optimally either divides equally the resources across groups, or concentrates entirely on one group, depending on whether there is positive or negative assortativity, respectively. We study a game in which agents can, at a cost, immunize. Negative assortative interactions generate highly asymmetric equilibrium outcomes between ex-ante identical groups. When groups have an underlying difference, even a small amount of inter-group contacts generates large asymmetries. We study the diffusion of a harmful state through a population. Immunity is available, but is costly. The state is meant to capture various kinds of choices or risky behaviors such as, for example, tobacco use, in which case immunity is interpreted as a commitment to avoid the temptation of smoking. The state can also capture the presence of an electronic virus on a computer network; in this case immunity represents the purchase of anti-virus software, or other costly measures taken to avoid the virus. But perhaps the most conventional interpretation is that the state represents human infection of various communicable diseases that spread through social contacts; in this case immunity captures a decision to vaccinate oneself