Social distance and network structures

This paper proposes a tractable model that allows us to analyze how agents' perception of relationships with others determines the structures of networks. In our model, agents are endowed with their own multidimensional characteristics and their payoffs depend on the social distance between them. We characterize the clustering coefficient and average path length in stable networks, and analyze how they are related to the way agents measure social distances. The model predicts the small-world properties under a class of social distance that violates the triangle inequality. Allowing for heterogeneity in link-formation costs, the model also accommodates other well documented empirical patterns of social networks such as skewed degree distributions, positive assortativity of degrees, and clustering-degree correlation.