A quick MST-based algorithm to obtain Pathfinder networks (∞, n-1)

Network scaling algorithms such as the Pathfinder algorithm are used to prune many different kinds of networks, including citation networks, random networks, and social networks. However, this algorithm suffers from run time problems for large networks and online processing due to its O(n(4)) time complexity. In this article, we introduce a new alternative, the MST-Pathfinder algorithm, which will allow us to prune the original network to get its PFNET(infinity, n - 1) in just O(n(2).log n) time. The underlying idea comes from the fact that the union (superposition) of all the Minimum Spanning Trees extracted from a given network is equivalent to the PFNET resulting from the Pathfinder algorithm parameterized by a specific set of values (r = infinity and q = n - 1), those usually considered in many different applications. Although this property is well-known in the literature, it seems that no algorithm based on it has been proposed, up to now, to decrease the high computational cost of the original Pathfinder algorithm. We also present a mathematical proof of the correctness of this new alternative and test its good efficiency in two different case studies: one dedicated to the post-processing of large random graphs, and the other one to a real world case in which medium networks obtained by a cocitation analysis of the scientific domains in different countries are pruned.