# Quick Detection of Nodes with Large Degrees

1 MAESTRO - Models for the performance analysis and the control of networks
CRISAM - Inria Sophia Antipolis - Méditerranée
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 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.
Keywords :
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Reports

https://hal.inria.fr/hal-00670278
Contributor : Konstantin Avrachenkov Connect in order to contact the contributor
Submitted on : Wednesday, February 15, 2012 - 10:05:05 AM
Last modification on : Thursday, September 24, 2020 - 10:22:03 AM
Long-term archiving on: : Wednesday, May 16, 2012 - 2:20:41 AM

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RR-7881.pdf
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### Identifiers

• HAL Id : hal-00670278, version 1
• ARXIV : 1202.3261

### Citation

Konstantin Avrachenkov, Nelly Litvak, Marina Sokol, Don Towsley. Quick Detection of Nodes with Large Degrees. [Research Report] RR-7881, INRIA. 2012. ⟨hal-00670278⟩

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