Abstract
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 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.
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This research was sponsored by INRIA Alcatel-Lucent Joint Lab, by the NSF under CNS-1065133, and the U.S. Army Research Laboratory under Cooperative Agreement W911NF-09-2-0053.
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Avrachenkov, K., Litvak, N., Sokol, M., Towsley, D. (2012). Quick Detection of Nodes with Large Degrees. In: Bonato, A., Janssen, J. (eds) Algorithms and Models for the Web Graph. WAW 2012. Lecture Notes in Computer Science, vol 7323. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30541-2_5
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DOI: https://doi.org/10.1007/978-3-642-30541-2_5
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