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arXiv · 1911.06737

On a Centrality Maximization Game

Maria Castaldo·Costanza Catalano·Giacomo Como·Fabio Fagnani
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Abstract

The Bonacich centrality is a well-known measure of the relative importance of nodes in a network. This notion is, for example, at the core of Google's PageRank algorithm. In this paper we study a network formation game where each player corresponds to a node in the network to be formed and can decide how to rewire his m out-links aiming at maximizing his own Bonacich centrality, which is his utility function. We study the Nash equilibria (NE) and the best response dynamics of this game and we provide a complete classification of the set of NE when m=1 and a fairly complete classification of the NE when m=2. Our analysis shows that the centrality maximization performed by each node tends to create undirected and disconnected or loosely connected networks, namely 2-cliques for m=1 and rings or a special "Butterfly"-shaped graph when m=2. Our results build on locality property of the best response function in such game that we formalize and prove in the paper.

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Maria Castaldo, Costanza Catalano, Giacomo Como, Fabio Fagnani. 2019-11-15. On a Centrality Maximization Game. https://arxiv.org/abs/1911.06737

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