When Engagement Meets Similarity: Efficient (k,r)-Core Computation on Social Networks Fan Zhang‡†, Ying Zhang†,LuQin†, Wenjie Zhang§, uXuemin Lin‡§ ‡East China Normal University, †CAI, University of Technology Sydney, §University of New South Wales
[email protected], {ying.zhang, lu.qin}@uts.edu.au, {zhangw, lxue}@cse.unsw.edu.au ABSTRACT Engagement. It is a common practice to encourage the engage- In this paper, we investigate the problem of (k,r)-core which in- ment of the group members by using the positive influence from tends to find cohesive subgraphs on social networks considering their friends in the same group (e.g., [3, 11, 21, 22, 29]); that is, both user engagement and similarity perspectives. In particular, we ensure there are a considerable number of friends for each individ- adopt the popular concept of k-core to guarantee the engagement ual user (vertex) in the group (subgraph). In [3], Bhawalkar and of the users (vertices) in a group (subgraph) where each vertex in a Kleinberg et al. use the game-theory to formally demonstrate that (k,r)-core connects to at least k other vertices. Meanwhile, we con- the popular k-core model can lead to a stable group (i.e., a cohe- sider the pairwise similarity among users based on their attributes. sive subgraph regarding graph structure). In this paper, we adopt Efficient algorithms are proposed to enumerate all maximal (k,r)- the k-core model on the graph structure, where each vertex in the cores and find the maximum (k,r)-core, where both problems are subgraph has at least k neighbors (structure constraint).