Mixing Time of Exponential Random Graphs

A plethora of random graph models have been developed in recent years to study a range of problems on networks, driven by the wide availability of data from many social, telecommunication, biochemical and other networks. A key model, extensively used in the sociology literature, is the exponential random graph model. This model seeks to incorporate in random graphs the notion of reciprocity, that is, the larger than expected number of triangles and other small subgraphs. Sampling from these distributions is crucial for answering almost any problem of parameter estimation hypothesis testing or to understand the inherent network model itself. In practice this sampling is typically carried out using either the Glauber dynamics or the Metropolis-Hasting Markov chain Monte Carlo procedure. In this paper we characterize the high and low temperature regimes. We establish that in the high temperature regime the mixing time of the Glauber dynamics is Θ(n2 log n), where n is the number of vert...

• Type: Conference
• Year: 2008
• Where: FOCS
• Authors: Shankar Bhamidi, Guy Bresler, Allan Sly
• Keywords: FOCS 2008, Random Graph, Random Graph Model, Temperature Regime, Theoretical Computer Science