Quick detection of nodes with large degrees

Konstantin Avrachenkov, Nelly Litvak, Marina Sokol, Don Towsley

9 Citations (Scopus)

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 $\mathcal{O}(n)$ , 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.
Original language English 1-19 19 Internet mathematics 10 1-2 https://doi.org/10.1080/15427951.2013.798601 Published - 5 May 2014

Keywords

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