Continuous Homophily and Clustering in Random Networks

Abstract

We propose a random network model incorporating heterogeneity of agents and a continuous notion of homophily. Unlike the vast majority of the corresponding economic literature, we capture homophily in terms of similarity rather than equality of agents. We show that if links between similar agents are indeed more likely, our homophilous random network model exhibits clustering. Moreover, simulations indicate that the well-known small-world phenomenon is preserved even at high homophily levels. As a possible application we provide a stylized labor market model, where a firm can hire a worker via the social network.

From Acquaintances to Friends: Homophily and Learning in Networks

“…Gauer and Landwehr (2015) assume that formation follows a Bernoulli Random Graph model in which the probability of a link between two agents is greater when agent types are closer together. There is no learning and no active decision making by agents; linking is entirely a random process.…”

“…In this sense, the learned information network will always be a subnetwork of the complete information network , which is defined as the network between all pairs of agents with types closer than ignoring capacity constraints. 9 Thus we want to study the effect of a removal of links from on the final network * , where the removal is due to errors in learning in the experimentation phase. We will do so via Monte Carlo simulations.…”

Stochastic Network Formation and Homophily

“…In this way every node i is characterized a vector α i ∈ R m , where m is the number of characteristics that we consider, and we can think of i as a point in an m-dimensional space, that can be endowed with many possible metrics. In this setting, Gauer and Landwehr (2014) and Iijima and Kamada (2014) are two recent theoretical papers which assume that the probability of linking p(i, j), of two nodes i and j, depends in a monotonic decreasing way on their distance in this m-dimensional space. The two approaches differ in the distance metric they consider: Gauer and Landwehr (2014) consider the Euclidean distance when m = 1, while Iijima and Kamada (2014) adopts the k'th norms, in which the distance between two points in the type space is the k'th smallest distance among the m dimension-wise distances between them.…”