Multiscale community geometry in a network and its application.

We introduce a between-ness-based distance metric to extract local and global information for each pair of nodes (or "vertices" used interchangeably) located in a binary network. Since this distance then superimposes a weighted graph upon such a binary network, a multiscale clustering mechanism, called data cloud geometry, is applicable to discover hierarchical communities within a binary network. This approach resolves many shortcomings of community finding approaches, which are primarily based on modularity optimization. Using several contrived and real binary networks, our community hierarchies compare favorably with results derived from a recently proposed approach based on time-scale differences of random walks and has already demonstrated significant improvements over module-based approaches, especially on the multiscale and the determination of the number of communities.