Detecting Topological Changes in Dynamic Community Networks

TL;DR

This paper introduces a method to detect significant topological changes in dynamic community networks by analyzing a stochastic blockmodel extension, enabling early detection of abnormal community merging events.

Contribution

It provides a detailed analysis of a dynamic community graph model and proposes a topology-based change detection method that does not require community decomposition.

Findings

The proposed test detects topological changes effectively in simulated dynamic graphs.

Theoretical analysis supports the validity of the change detection method.

Monte Carlo simulations demonstrate the method's ability to identify abnormal community merging.

Abstract

The study of time-varying (dynamic) networks (graphs) is of fundamental importance for computer network analytics. Several methods have been proposed to detect the effect of significant structural changes in a time series of graphs. The main contribution of this work is a detailed analysis of a dynamic community graph model. This model is formed by adding new vertices, and randomly attaching them to the existing nodes. It is a dynamic extension of the well-known stochastic blockmodel. The goal of the work is to detect the time at which the graph dynamics switches from a normal evolution -- where balanced communities grow at the same rate -- to an abnormal behavior -- where communities start merging. In order to circumvent the problem of decomposing each graph into communities, we use a metric to quantify changes in the graph topology as a function of time. The detection of anomalies becomes one of testing the hypothesis that the graph is undergoing a significant structural change. In addition the the theoretical analysis of the test statistic, we perform Monte Carlo simulations of our dynamic graph model to demonstrate that our test can detect changes in graph topology.