Manipulating Structural Graph Clustering

Structural graph clustering (SCAN) is a popular clustering technique. Using the concept of$\epsilon$-neighborhood, SCAN defines the core vertices that uniquely determine the clusters of a graph. Most existing studies assume that the graph processed by SCAN contains no controlled edges. Few studies, however, have focused on manipulating SCAN by injecting edges. Manipulation of SCAN can be used to assess its robustness and lay the groundwork for developing robust clustering algorithms. To fill this gap and considering the importance of the$\epsilon$-neighborhood for SCAN, we propose a problem, denoted as MN, for manipulating SCAN. The MN problem aims to maximize the$\epsilon$-neighborhood of the target vertex by inserting some edges. On the theoretical side, we prove that the MN problem is both NP-hard and APX-hard, and also is non-submodular and non-monotonic. On the algorithmic side, we design an algorithm by focusing on how to select vertices to join$\epsilon -$neighborhood and thus avoid enumerating edges to report a solution. As a result, our algorithm bypasses the non-monotonicity nature of the MN problem. Extensive experiments on real-world graphs show that our algorithm can effectively solve the proposed MN problem.