Modularity-driven clustering of dynamic graphs

Authors:
Robert Görke;Pascal Maillard;Christian Staudt;Dorothea Wagner
Affiliations:
Institute of Theoretical Informatics, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany;Laboratoire de Probabilités et Modèles Aléatoires, Université Pierre et Marie Curie (Paris VI), Paris, France;Institute of Theoretical Informatics, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany;Institute of Theoretical Informatics, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
Venue:
SEA'10 Proceedings of the 9th international conference on Experimental Algorithms
Year:
2010

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Abstract

Maximizing the quality index modularity has become one of the primary methods for identifying the clustering structure within a graph. As contemporary networks are not static but evolve over time, traditional static approaches can be inappropriate for specific tasks. In this work we pioneer the NP-hard problem of online dynamic modularity maximization. We develop scalable dynamizations of the currently fastest and the most widespread static heuristics and engineer a heuristic dynamization of an optimal static algorithm. Our algorithms efficiently maintain a modularity-based clustering of a graph for which dynamic changes arrive as a stream. For our quickest heuristic we prove a tight bound on its number of operations. In an experimental evaluation on both a real-world dynamic network and on dynamic clustered random graphs, we show that the dynamic maintenance of a clustering of a changing graph yields higher modularity than recomputation, guarantees much smoother clustering dynamics and requires much lower runtimes. We conclude with giving recommendations for the choice of an algorithm.