  A popular model to measure the stability of a network is k-core - the maximal
induced subgraph in which every vertex has at least k neighbors. Many studies
maximize the number of vertices in k-core to improve the stability of a
network. In this paper, we study the edge k-core problem: Given a graph G, an
integer k and a budget b, add b edges to non-adjacent vertex pairs in G such
that the k-core is maximized. We prove the problem is NP-hard and APX-hard. A
heuristic algorithm is proposed on general graphs with effective optimization
techniques. Comprehensive experiments on 9 real-life datasets demonstrate the
effectiveness and the efficiency of our proposed methods.
