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This paper examines a schema for graph-theoretic clustering using node-based resilience measures. Node-based resilience measures optimize an objective based on a critical set of nodes whose removal causes some severity of disconnection in the network. Beyond presenting a general framework for the usage of node based resilience measures for variations of clustering problems, we experimentally validate the usefulness of such methods in accomplishing the following: (i) clustering a graph in one step without knowing the number of clusters a priori; (ii) removing noise from noisy data; and (iii) detecting overlapping communities. We demonstrate that this clustering schema can be applied successfully using a wide range of data, including both real and synthetic networks, both natively in graph form and also expressed as point sets.

Node-Based Resilience Measure Clustering with Applications to Noisy and Overlapping Communities in Complex Networks