Axiomatic Characterization of Game-Theoretic Centrality

Abstract


 
 
 One of the fundamental research challenges in network science is centrality analysis, i.e., identifying the nodes that play the most important roles in the network. In this article, we focus on the game-theoretic approach to centrality analysis. While various centrality indices have been recently proposed based on this approach, it is still unknown how general is the game-theoretic approach to centrality and what distinguishes some game-theoretic centralities from others. In this article, we attempt to answer this question by providing the first axiomatic characterization of game-theoretic centralities. Specifically, we show that every possible centrality measure can be obtained following the game-theoretic approach. Furthermore, we study three natural classes of game-theoretic centrality, and prove that they can be characterized by certain intuitive properties pertaining to the well-known notion of Fairness due to Myerson.
 
 

Random Walk Decay Centrality

“…Our paper belongs to a line of papers that study the axiomatic properties of centrality measures (Boldi and Vigna 2014;Bloch, Jackson, and Tebaldi 2016;Skibski, Michalak, and Rahwan 2018). In particular, our axiomatization of the Decay centrality relies on a recent axiomatization for undirected graphs proposed by Skibski and Sosnowska (2018).…”

A Generic Axiomatic Characterization for Measuring Influence in Social Networks

“…Research has also been done on the axiomatic foundations for ranking systems in a directed graph [Altman and Tennenholtz(2008)] in the context of Page Rank and voting ranking systems. Recently an axiomatic framework for game-theoretic network centralities [Skibski et al(2017) Skibski, Michalak, and Rahwan] is proposed, where the authors establish a link between the game-theoretic centrality measures and classical centrality measures. Naturally the inherent set up of their analysis is significantly different from our framework.…”

“…Though these centrality measures offer new insights, the lack of a theoretical underpinning makes it difficult to choose the right centrality measure for a given context. Towards this end, there exists some effort in the literature [Skibski et al(2017) Skibski, Michalak, and Rahwan], [Altman and Tennenholtz(2008)], [Boldi and Vigna(2014)], [Skibski et al(2016) Skibski, Rahwan, Michalak, and Yokoo] in terms of developing axiomatic frameworks to better understand the properties of these centrality measures. However, these theoretical explorations are limited to only certain specific scenarios.…”

Fair division in the presence of externalities

“…The Shapley value is used not only to divide costs or share profits in cooperative scenarios, but also as an advanced tool in various other settings, such as assessing the role of a criterion in multi-criteria decision making (Grabisch et al 2008), attributing risk in public health applications (Cox 1985), and evaluating centrality of nodes in networks (Gómez et al 2003;Skibski et al 2018a).…”