Generating functions and the Myerson vector in communication networks

Мазалов, Владимир; Trukhina, Lyudmila I.

doi:10.1515/dma-2014-0026

Cited by 16 publications

(19 citation statements)

References 6 publications

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“…Characteristic function (payoff of coalition S) can be determined in different ways. Here we use the approach of [10,11,14,15], which is based on discounting directed paths. The payoff to an individual player is called an imputation.…”

Section: Myerson Cooperative Game Approachmentioning

confidence: 99%

Cooperative Game Theory Approaches for Network Partitioning

Avrachenkov

Kondratev

Мазалов

2017

Lecture Notes in Computer Science

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The paper is devoted to game-theoretic methods for community detection in networks. The traditional methods for detecting community structure are based on selecting denser subgraphs inside the network. Here we propose to use the methods of cooperative game theory that highlight not only the link density but also the mechanisms of cluster formation. Specifically, we suggest two approaches from cooperative game theory: the first approach is based on the Myerson value, whereas the second approach is based on hedonic games. Both approaches allow to detect clusters with various resolution. However, the tuning of the resolution parameter in the hedonic games approach is particularly intuitive. Furthermore, the modularity based approach and its generalizations can be viewed as particular cases of the hedonic games.

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Section: Myerson Cooperative Game Approachmentioning

confidence: 99%

Cooperative Game Theory Approaches for Network Partitioning

Avrachenkov

Kondratev

Мазалов

2017

Lecture Notes in Computer Science

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“…where σ k (i) is a number of the paths of the length k which include i. In [15] it is proven that this allocation rule for unweighted graphs is the Myerson value. The Myerson value for player i depends on the number of paths that it lies on.…”

Section: Centrality Measure For Weighted Network Using Myerson Valuementioning

confidence: 99%

“…But computing the Myerson value is not an easy problem. In the paper [15] a sufficiently simple procedure was proposed to calculate the Myerson value for a cooperative game on the unweighted graph with special characteristic function.…”

Section: Introductionmentioning

confidence: 99%

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Game-Theoretic Centrality Measures for Weighted Graphs

Mazalov

Avrachenkov²,

Трухина

et al. 2016

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The betweenness centrality is one of the basic concepts in the analysis of the social networks. Initial definition for the betweenness of a node in the graph is based on the fraction of the number of geodesics (shortest paths) between any two nodes that given node lies on, to the total number of the shortest paths connecting these nodes. This method has polynomial complexity. We propose a new concept of the betweenness centrality for weighted graphs using the methods of cooperative game theory. The characteristic function is determined by special way for different coalitions (subsets of the graph). Two approaches are used to determine the characteristic function. In the first approach the characteristic function is determined via the number of direct and indirect weighted connecting paths in the coalition. In the second approach the coalition is considered as an electric network and the characteristic function is determined as a total current in this network. We use the Kirchhoff's law. After that the betweenness centrality is determined as the Myerson value. The results of computer simulations for some examples of networks, in particular, for the popular social network "VKontakte", as well as the comparing with the PageRank method are presented.

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“…The imputation of the general payoff in this cooperative game can be used for ranking of players and, respectively, for nodes of the graph. In [17] for the communication game with special characteristic function it was proposed a fairly simple imputation procedure based on the generating function and was shown that the resulting imputation agrees with the Myerson value. The advantage of the Myerson value is in taking into account the impact of all coalitions.…”

Section: Introductionmentioning

confidence: 99%

Beta Current Flow Centrality for Weighted Networks

Avrachenkov¹,

Mazalov²,

Tsynguev³

2015

Computational Social Networks

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Betweenness centrality is one of the basic concepts in the analysis of social networks. Initial definition for the betweenness of a node in a graph is based on the fraction of the number of geodesics (shortest paths) between any two nodes that given node lies on, to the total number of the shortest paths connecting these nodes. This method has quadratic complexity and does not take into account indirect paths. We propose a new concept of betweenness centrality for weighted network, beta current flow centrality, based on Kirchhoff's law for electric circuits. In comparison with the original current flow centrality and alpha current flow centrality, this new measure can be computed for larger networks. The results of numerical experiments for some examples of networks, in particular, for the popular social network VKontakte as well as the comparison with PageRank method are presented.

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Generating functions and the Myerson vector in communication networks

Cited by 16 publications

References 6 publications

Cooperative Game Theory Approaches for Network Partitioning

Cooperative Game Theory Approaches for Network Partitioning

Game-Theoretic Centrality Measures for Weighted Graphs

Beta Current Flow Centrality for Weighted Networks

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