K-core Minimization: An Edge Manipulation Approach

In social networks, dense relationships among users contribute to stable networks. Breakdowns of some relationships may cause users to leave the network hence decrease the network stability. A popular metric to measure the stability of a network is k-core, i.e., the maximal subgraph of a social network in which each node has at least k neighbors. In this paper, we propose a novel problem, called k-core minimization. Given a graph G, an integer k and a budget b, we aim to identify a set B of edges with size b, so that we can get the minimum k-core by deleting B from G. We first formally define the problem and prove its NP-hardness. Then a baseline greedy algorithm is proposed. To handle large graphs, an optimized algorithm, named KC-Edge, is developed by adopting novel pruning rules. Finally, comprehensive experiments on 6 real social networks are conducted to demonstrate the efficiency and effectiveness of our proposed methods.

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