Efficient computation of the Shapley value for game-theoretic network centrality

The Shapley value—probably the most important normative payoff division scheme in coalitional games—has recently been advocated as a useful measure of centrality in networks. However, although this approach has a variety of real-world applications (including social and organisational networks, biological networks and communication networks), its computational properties have not been widely studied. To date, the only practicable approach to compute Shapley value-based centrality has been via Monte Carlo simulations which are computationally expensive and not guaranteed to give an exact answer. Against this background, this paper presents the first study of the computational aspects of the Shapley value for network centralities. Specifically, we develop exact analytical formulae for Shapley value-based centrality in both weighted and unweighted networks and develop efficient (polynomial time) and exact algorithms based on them. We empirically evaluate these algorithms on two real-life examples (an infrastructure network representing the topology of the Western States Power Grid and a collaboration network from the field of astrophysics) and demonstrate that they deliver significant speedups over the Monte Carlo approach. Fo

Enhancing the navigability in a social network of smart objects: a Shapley-value based approach

The Internet of Things (IoT) holds the promise to interconnect any possible object capable of providing useful information about the physical world for the benefit of humans' quality of life. The increasing number of heterogeneous objects that the IoT has to manage introduces crucial scalability issues that still need appropriate solutions. In this respect, one promising proposal is the Social IoT (SIoT) paradigm, whose main principle is to enable objects to autonomously establish social links with each other (adhering to rules set by their owners). "Friend" objects exchange data in a distributed manner and this avoids centralized solutions to implement major functions, such as: node discovery, information search, and trustworthiness management. However, the number and types of established friendships affect network navigability. This issue is the focus of this paper, which proposes an efficient, distributed and dynamic solution for the objects to select the right friends for the benefit of the overall network connectivity. The proposed friendship selection mechanism relies on a game theoretic model and a Shapley-value based algorithm. Two different utility functions are defined and evaluated based on either a group degree centrality and an average local clustering parameter. The comparison in terms of global navigability is measured in terms of average path length for the interconnection of any couple of nodes in the network. Results show that the group degree centrality brings to an enhanced degree of navigability thanks to the ability to create a suitable core of hubs