In this paper, we investigate the problem of (k,r)-core which intends to find cohesive subgraphs on social networks considering both user engagement and similarity perspectives. In particular, we adopt the popular concept of k-core to guarantee the engagement of the users (vertices) in a group (subgraph) where each vertex in a (k,r)-core connects to at least k other vertices. Meanwhile, we consider the pairwise similarity among users based on their attributes. Efficient algorithms are proposed to enumerate all maximal (k,r)cores and find the maximum (k,r)-core, where both problems are shown to be NP-hard. Effective pruning techniques substantially reduce the search space of two algorithms. A novel (k,k )-core based (k,r)-core size upper bound enhances performance of the maximum (k,r)-core computation. We also devise effective search orders for two mining algorithms where search priorities for vertices are different. Comprehensive experiments on real-life data demonstrate that the maximal/maximum (k,r)-cores enable us to find interesting cohesive subgraphs, and performance of two mining algorithms is effectively improved by proposed techniques.
REF aim to find (k, r )-cores in attributed graphs, a (k, r )-cores is a connected subgraph where each vertex is connected to at least k vertices and the similarity between attributes values is higher than a minimum threshold r .
When Engagement Meets Similarity: Efficient (k, r)-Core Computation on Social Networks
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Computer Science Mathematics