https://hal.inria.fr/hal-00764220Avrachenkov, KonstantinKonstantinAvrachenkovMAESTRO - Models for the performance analysis and the control of networks - CRISAM - Inria Sophia Antipolis - Méditerranée - Inria - Institut National de Recherche en Informatique et en AutomatiqueLitvak, NellyNellyLitvakEEMCS - Faculty of Electrical Engineering, Mathematics and Computer Science [Twente] - University of Twente [Netherlands]Sokol, MarinaMarinaSokolMAESTRO - Models for the performance analysis and the control of networks - CRISAM - Inria Sophia Antipolis - Méditerranée - Inria - Institut National de Recherche en Informatique et en AutomatiqueTowsley, DonDonTowsleyDepartment of Computer Science [Amherst] - UMASS - University of Massachusetts SystemQuick Detection of Nodes with Large DegreesHAL CCSD2012[INFO.INFO-NI] Computer Science [cs]/Networking and Internet Architecture [cs.NI]Avrachenkov, KonstantinAnthony Bonato and Jeannette Janssen2012-12-12 15:49:562022-01-20 17:27:372012-12-12 16:04:04enConference papershttps://hal.inria.fr/hal-00764220/document10.1007/978-3-642-30541-2_5application/pdf1Our goal is to quickly find top $k$ lists of nodes with the largest degrees in large complex networks. 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 $\mbox{O}(n)$, 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 the 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 which requires very little knowledge about the structure of the network.