Refining Social Graph Connectivity via Shortcut Edge Addition

Abstract

Small changes on the structure of a graph can have a dramatic effect on its connectivity. While in the traditional graph theory, the focus is on well-defined properties of graph connectivity, such as biconnectivity, in the context of a social graph , connectivity is typically manifested by its ability to carry on social processes . In this paper, we consider the problem of adding a small set of nonexisting edges ( shortcuts ) in a social graph with the main objective of minimizing its characteristic path length . This property determines the average distance between pairs of vertices and essentially controls how broadly information can propagate through a network. We formally define the problem of interest, characterize its hardness and propose a novel method, path screening , which quickly identifies important shortcuts to guide the augmentation of the graph. We devise a sampling-based variant of our method that can scale up the computation in larger graphs. The claims of our methods are formally validated. Through experiments on real and synthetic data, we demonstrate that our methods are a multitude of times faster than standard approaches, their accuracy outperforms sensible baselines and they can ease the spread of information in a network, for a varying range of conditions.