Quick detection of nodes with large degrees

Konstantin Avrachenkov, Nelly Litvak, Marina Sokol, Don Towsley

Research output: Book/ReportReportProfessional

8 Citations (Scopus)
85 Downloads (Pure)


Our 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 a node with the largest degree 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.
Original languageEnglish
Place of PublicationSophia Antipolis, France
Number of pages13
Publication statusPublished - Feb 2012

Publication series

NameResearch Report / INRIA, ISSN 0249-6399
ISSN (Print)0249-6399


  • Stopping criteria
  • Top $k$ list
  • Random walk
  • Complex networks
  • Detection of nodes with the largest degrees


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