Quick detection of nodes with large degrees

Konstatin Avrachenkov, Nelly Litvak, Marina Sokol, Don Towsley

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7 Citations (Scopus)
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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

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Complex networks
Complex Networks
Random walk
Vertex of a graph
Average Complexity
Stopping Criterion
Adjacency
Deterministic Algorithm
Numerical Experiment
Experiments

Keywords

• Random walk
• Detection of nodes with the largest degrees
• METIS-306037
• Stopping criteria
• EWI-25090
• Top $k$ list
• Complex networks
• IR-91970

Cite this

Avrachenkov, Konstatin ; Litvak, Nelly ; Sokol, Marina ; Towsley, Don. / Quick detection of nodes with large degrees. In: Internet mathematics. 2014 ; Vol. 10, No. 1-2. pp. 1-19.
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Quick detection of nodes with large degrees. / Avrachenkov, Konstatin; Litvak, Nelly; Sokol, Marina; Towsley, Don.

In: Internet mathematics, Vol. 10, No. 1-2, 05.05.2014, p. 1-19.

Research output: Contribution to journalArticleAcademicpeer-review

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AU - Avrachenkov, Konstatin

AU - Litvak, Nelly

AU - Sokol, Marina

AU - Towsley, Don

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AB - 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.

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