Abstract : Our goal is to find top-k lists of nodes with the largest degrees in large complex networks quickly. If the adjacency list of the network is known (not often the case in complex networks), a deterministic algorithm to find the top-k list of nodes with the largest degrees requires an average complexity of O(n), where n is the number of nodes in the network. Even this modest complexity can be very high for large complex networks. We propose to use a random-walk-based method. We show theoretically and by numerical experiments that for large networks, the random-walk method finds good-quality top lists of nodes with high probability and with computational savings of orders of magnitude. We also propose stopping criteria for the random-walk method that requires very little knowledge about the structure of the network.
Konstantin Avrachenkov, Nelly Litvak, Marina Sokol, Don Towsley. Quick Detection of Nodes with Large Degrees. Internet Mathematics, Taylor & Francis, 2014, 10 (1-2), pp.1-19. ⟨10.1080/15427951.2013.798601⟩. ⟨hal-01092304⟩