Efficient Computation of Importance Based Communities in Web-Scale Networks Using a Single Machine

Finding decompositions of a graph into a family of communities is crucial to understanding its underlying structure. Algorithms for finding communities in networks often rely only on structural information and search for cohesive subsets of nodes. In practice however, we would like to find communities that are not only cohesive, but also influential or important. In order to capture such communities, Li, Qin, Yu, and Mao introduced a novel community model called "k-influential community" based on the concept of $k$-core, with numerical values representing "influence" assigned to the nodes. They formulate the problem of finding the top-r most important communities as finding r connected k-core subgraphs ordered by the lower-bound of their importance. In this paper, our goal is to scale-up the computation of top-r, k-core communities to web-scale graphs of tens of billions of edges. We feature several fast new algorithms for this problem. With our implementations, we show that we can efficiently handle massive networks using a single consumer-level machine within a reasonable amount of time.