Exploring Finer Granularity within the Cores: Efficient (k,p)-Core Computation

In this paper, we propose and study a novel cohesive subgraph model, named (k,p)-core, which is a maximal subgraph where each vertex has at least k neighbours and at least p fraction of its neighbours in the subgraph. The model is motivated by the finding that each user in a community should have at least a certain fraction p of neighbors inside the community to ensure user engagement, especially for users with large degrees. Meanwhile, the uniform degree constraint k, as applied in the k-core model, guarantees a minimum level of user engagement in a community, and is especially effective for users with small degrees. We propose an O(m) algorithm to compute a (k,p)-core with given k and p, and an O(dm) algorithm to decompose a graph by (k,p)-core, where m is the number of edges in the graph G and d is the degeneracy of G. A space efficient index is designed for time-optimal (k,p)-core query processing. Novel techniques are proposed for the maintenance of (k,p)-core index against graph dynamic. Extensive experiments on 8 reallife datasets demonstrate that our (k,p)-core model is effective and the algorithms are efficient.