Coarse-Graining Network Dynamics: The Adaptive SIS Model

Abstract

The problem of extending data-mining techniques for use with graph objects is investigated through the application of diffusion maps to graph object datasets. Various ways of quantifying graph similarity, also known as the graph matching problem, are studied, and a candidate distance function on labelled graphs is proposed. The metric's suitability is validated by application to a model of disease proliferation, which is based on the susceptible-infected-susceptible (SIS) epidemiological framework. By using only sampled instances of a random network, evolving according to a predefined set of rules, we use diffusion maps to extract the important variables that define the system's long term dynamics in the oscillatory phase. Moreover, we also demonstrate that these extracted variables are actually reparametrizations of the coarse variables known to define this system, providing further evidence that this data-mining technique can successfully extract the important information inherent to graph object datasets.