“Centrality in Stochastic Networks”

Teaser: In many economic and managerial applications, there is an underlying network of connections that governs a dynamical system. In some cases, variables of interest (e.g., steady-state beliefs) can be reduced to characterizing centrality measures on the network. To predict these centrality measures, how important is network knowledge? We find that knowledge of high-level statistics about the network are typically important, but information about individual links often provides little added value.

Abstract: Centrality measures are ubiquitous, appearing in models of opinion formation, macroeconomics, and consumption with externalities. With few exceptions, most of the previous literature has focused on modeling centrality in settings where the underlying network structure is known and remains static. This paper expands on this work by considering arbitrary row-stochastic random networks that may be evolving over time. Under mild assumptions, we show that all centrality measures are, with high probability, close to their values in an appropriately-defined “average” network. We conclude by demonstrating how this result offers a major technical simplification for the dynamic and stochastic analyses of several applications.