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, although the average distance between agents

increases in homophily, 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.