Research on collapsed (α, k)-NP-community on signed graph

In social network, the departure of critical users can lead to the disintegration of the entire community, i.e., lead a large number of other users to drop out. This paper aims to find the critical users in the community and prevent the whole community from disintegrating. Most of the other research work is carried out on the unsigned network. In this paper, we study this problem on a signed network and propose a new community model (α, k)-NP-community. Specifically, the nodes in the community model should satisfy the maximum subgraph with no less than ak good friends (positive neighbor) and no more than k enemy (negative neighbor). We propose an effective algorithm to find (α, k)-NP-community. In order to identify the critical users of (α, k)-NP-community, we propose the problem of collapsed (α, k)-NP-community: given a signed graph G, integers α, k, our goal is to find such nodes in graph G, the departure of the best collapser will lead to the smallest (α, k)-NP-community. We prove that the problem is NP-hard. Finally, we present two lemmas to apply the αKCA algorithm, which effectively reduced the number of candidate nodes and accelerated the search process. The results of extensive experiments on four real datasets demonstrate the effectiveness and efficiency of our algorithms.