Analyzing Social Networks as Stochastic Processes

Abstract

This article presents a new methodology for studying a social network of interpersonal relationships, based on stochastic modeling of the changes that occur in the network over time. Specifically, we postulate that these changes can be modeled as a continuous-time Markov chain. The transition rates for the chain are dependent on a small set of parameters that measure the importance of various aspects of social structure on the probability of change. We discuss the assumptions of the framework and describe two simple models that are applications of it. We then present, analyze, and interpret several examples, and we outline methods of parameter estimation. The models prove to be quite effective and allow us to better understand the evolution of a network.

Key Words:

• Directed graphs
• Stochastic modeling
• Continuous-time Markov chains
• Statistical inference for stochastic processes