Continuous homophily and clustering in random networks

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 by assuming that the probability of linkage between two agents continuously decreases in the distance of their characteristics. A homophily parameter directly determines the strength of this effect. As a main result, we show that for any positive level of homophily our model exhibits clustering, that is an increased probability of linkage given a common neighbor. As opposed to this, the seminal Bernoulli Random Graph model à la Erdős and Rényi (1959)is comprised as the limit case of no homophily. Moreover, simulations indicate that the well-known small-world phenomenon is preserved even at high homophily levels. We finally provide a possible application in form of a stylized labor market model, where a firm can hire a new employee via the social network.