The many facets of community detection in complex networks.
Michael T. Schaub,Michael T. Schaub,Michael T. Schaub,Jean-Charles Delvenne,Martin Rosvall,Renaud Lambiotte +5 more
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In this paper, the authors provide a focused review of the different motivations that underpin community detection, highlighting the different facets of community detection and highlighting the many lines of research and points out open directions and avenues for future research.Abstract:
Community detection, the decomposition of a graph into essential building blocks, has been a core research topic in network science over the past years. Since a precise notion of what constitutes a community has remained evasive, community detection algorithms have often been compared on benchmark graphs with a particular form of assortative community structure and classified based on the mathematical techniques they employ. However, this comparison can be misleading because apparent similarities in their mathematical machinery can disguise different goals and reasons for why we want to employ community detection in the first place. Here we provide a focused review of these different motivations that underpin community detection. This problem-driven classification is useful in applied network science, where it is important to select an appropriate algorithm for the given purpose. Moreover, highlighting the different facets of community detection also delineates the many lines of research and points out open directions and avenues for future research.read more
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Spectral partitioning works: planar graphs and finite element meshes
D.A. Spielmat,Shang-Hua Teng +1 more
TL;DR: It is proved that spectral partitioning techniques can be used to produce separators whose ratio of vertices removed to edges cut is O(/spl radic/n) for bounded-degree planar graphs and two-dimensional meshes and O(n/sup 1/d/) for well-shaped d-dimensional mesh.