Lyapunov-Based Anomaly Detection in Highly-Clustered Networks

Abstract

Network formation models explain the dynamics of the structure of connections using mechanisms that operate under different principles for establishing and removing edges. The Jackson–Rogers model is a generic framework that applies the principle of triadic closure to networks that grow by the addition of new nodes and new edges over time. Past work describes the limit distribution of the in-degree of the nodes based on a continuous-time approximation. Here, we introduce a discrete-time approach of the dynamics of the in- and out-degree distributions of a variation of the model. Furthermore, we characterize the limit distributions and the expected value of the average degree as equilibria, and prove that the equilibria are asymptotically stable. Finally, we use the stability properties of the model to propose a detection criterion for anomalies in the edge formation process.