Efficient Top-k edge structural diversity search

The structural diversity of an edge, which is measured by the number of connected components of the edge's ego-network, has recently been recognized as a key metric for analyzing social influence and information diffusion in social networks. Given this, an important problem in social network analysis is to identify top-k edges that have the highest structural diversities. In this work, we for the first time perform a systematical study for the top-k edge structural diversity search problem on large graphs. Specifically, we first develop a new online search framework with two basic upper-bounding rules to efficiently solve this problem. Then, we propose a new index structure using near-linear space to process the top-k edge structural diversity search in near-optimal time. To create such an index structure, we devise an efficient algorithm based on an interesting connection between our problem and the 4-clique enumeration problem. In addition, we also propose efficient index maintenance techniques to handle dynamic graphs. The results of extensive experiments on five large real-life datasets demonstrate the efficiency, scalability, and effectiveness of our algorithms.