Random Graphs and Social Networks: An Economics Perspective

This review of current research on networks emphasizes three strands of the literature on social networks. The first strand is composed of models of endogenous network formation from both the economics and the computer science literature. The review highlights the sen- sitive dependence of the topology of endogenous networks on parameters of the behavioral models employed. The second strand draws from the recent econophysics literature in order to review the recent revival of interest in the random graph theory. This mathematical tool allows one to study social networks that result from uncoordinated random action of indi- viduals in setting up connections with others. The review explores a number of examples to assess the potential of recent research on random graphs with arbitrary degree distributions in accommodating more general behavioral motivations for social network formation. The third strand focuses on a specific model of social networks, Markov random graphs, that is quite central in the mathematical sociology and spatial statistics literatures but little known outside those literatures. These are random graphs where the events that different edges are present are dependent, if edges are incident to the same node, and independent, otherwise. The paper assesses the potential for economic applications with this particular tool. The paper concludes with an assessment of observable consequences of optimizing behavior in networks for the purpose of estimation.