Clustering method incorporating network topology and dynamics

Clustering is useful in elucidating associations among agents of networks and has been advantageously applied in numerous fields including biology, chemistry, sociology, and economics. Most clustering algorithms have been applied to (weighted) networks with a fixed topology. However, many networks are constructed to simulate particular dynamics on them; e.g., transmission of disease, vehicular transportation, electricity supply, and economic transfers in financial markets. These dynamics affect the large-scale structure that emerges from the underlying network. We present a clustering method that incorporates not only the weighted network topology, but also the particular dynamics for an application domain. The approach is general and can be used with any dynamic process that can be simulated on a network. We apply this method to several networks to validate it: a benchmark network, various toy networks, and two large realistic synthetic networks. These span four, five, and two orders of magnitude in numbers of agents and links, and average degree, respectively, and possess vastly different degree distributions. The largest network includes over 580,000 agents and 13 million edges. The results show that different structures arise from variations in dynamics processes for a fixed network, and reflect the changes in the process itself. We observe a sharp transition from unclustered to well-clustered communities as dynamical parameters vary.