A Probabilistic Framework for Structural Analysis and Community Detection in Directed Networks - 2018


There's growing interest in structural analysis of directed networks. Two major points that require to be addressed are: 1) a proper and precise definition of the graph clustering and community detection problem in directed networks and a couple of) algorithm design and evaluation of community detection algorithms in directed networks. Motivated by these, we tend to develop a probabilistic framework for structural analysis and community detection in directed networks based on our previous work in undirected networks. By relaxing the belief from symmetric bivariate distributions in our previous work to bivariate distributions that have the identical marginal distributions in this Project, we can still formally outline varied notions for structural analysis in directed networks, including centrality, relative centrality, community, and modularity. We tend to also extend three commonly used community detection algorithms in undirected networks to directed networks: the hierarchical agglomerative algorithm, the partitional algorithm, and the fast unfolding algorithm. These are created potential by 2 modularity preserving and sparsity preserving transformations. In conjunction with the probabilistic framework, we have a tendency to show these three algorithms converge in a very finite variety of steps. In specific, we have a tendency to show that the partitional algorithm may be a linear time algorithm for massive sparse graphs. Moreover, the outputs of the hierarchical agglomerative algorithm and also the quick unfolding algorithm are guaranteed to be communities. These 3 algorithms will also be extended to general bivariate distributions with some minor modifications. We conjointly conduct numerous experiments by using 2 sampling strategies in directed networks: one) PageRank and a couple of) random walks with self-loops and backward jumps.

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