Computing the Diameters of Huge Social Networks

The diameter of a graph is the maximum distance among all pairs of nodes. Determining the diameter of a graph in the tradition way costs O(mn) time, where n is the number of nodes and m is the number of edges. A social network can be modelled as a graph. With the rapid expansion of social networks, the number of nodes in a social network could be hundreds of millions. In this paper, we propose a new approach for computing the diameters of large undirected unweighted graphs. The worst case time complexity is still O(mn). In practice, especially for social network graphs, the running time is O(m). Our approach is based on BFS to select a proper node as the starting node of a BFS process is the most important issue when computing the diameter. We show how to choose the good nodes with small cost.