## Module Detection in Directed Real-World Networks

Please always quote using this URN: urn:nbn:de:0297-zib-49849
• We investigate the problem of finding modules (or clusters, communities) in directed networks. Until now, most articles on this topic have been oriented towards finding complete network partitions despite the fact that this often is unwanted. We present a novel random walk based approach for non-complete partitions of the directed network into modules in which some nodes do not belong to only one of the modules but to several or to none at all. The new random walk process is reversible even for directed networks but inherits all necessary information about directions and structure of the original network. We demonstrate the performance of the new method in application to a real-world earthquake network.

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Author: Ralf Banisch, Christof Schütte, Natasa Djurdjevac Conrad ZIB-Report Module identification and classification; communication; cycle decomposition; directed networks 60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Jxx Markov processes / 60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) [See also 90B30, 91D10, 91D35, 91E40] 94-XX INFORMATION AND COMMUNICATION, CIRCUITS / 94Cxx Circuits, networks / 94C15 Applications of graph theory [See also 05Cxx, 68R10] 2014/05/07 ZIB-Report (14-13) 1438-0064

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