We investigate the preferential attachment graphs proceeding from the following two assumptions. The first one: the probability that a new vertex connects to a vertex i is proportional to an arbitrary nonnegative function f of a vertex degree k. The second assumption: a new vertex can have a...

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...

In a spatially embedded network, that is a network where nodes can be uniquely determined in a system of coordinates, links’ weights might be affected by metric distances coupling every pair of nodes (dyads). In order to assess to what extent metric distances affect relationships (link’s...

Modeling the evolution of networks is central to our understanding of large communication systems, and more general, modern economic and social systems. The research on social and economic networks is truly interdisciplinary and the number of proposed models is huge. In this survey we discuss a...

Recently there has been a growing interest in evolutionary models of play with endogenous interaction structure. We call such processes co-evolutionary dynamics of networks and play. We study a co-evolutionary process of networks and play in settings where players have diverse preferences. In...