Combinatorial insights and robustness analysis for clustering in dynamical networks

This paper studies a clustering phenomena that emerges from a dynamic network with bounded and non-linear interactions. Necessary and sufficient conditions are given describing when the network exhibits clustering. We introduce a synchronization coefficient to quantify whether a network is synchronizing or clustering and provide a robustness margin for clustering. A combinatorial description of the dynamic network clustering is provided that relates to optimal graph partitioning. Finally, the synchronization coefficient is also used for defining a set of critical disturbances that can cause the system to cluster.