A Game Theoretic Neighbourhood-Based Relevance Index

Abstract

Centrality measures are used in network analysis to identify the relevant elements in a network. Recently, several centrality measures based on coalitional game theory have been successfully applied to different kinds of biological networks, such as brain networks, gene networks, and metabolic networks. We propose an approach, using coalitional games, to the problem of identifying relevant genes in a biological network. Our model generalizes the notion of degree centrality, whose correlation with the relevance of genes for different biological functions is supported by several practical evidences in the literature. The new relevance index we propose is characterized by a set of axioms defined on gene networks and a formula for its computation is provided. Furthermore, an application to the analysis of a large co-expression network is shortly presented.

An application of the Shapley value to the analysis of co-expression networks

“…In the remaining of this paper, we introduce and discuss an application of the Shapley value aimed at measuring the potential of a gene in preserving the regulatory activity within a co-expression network. On a co-expression network built over a dataset from the literature, we show that the Shapley value of the coalitional game introduced in the paper (Cesari et al 2017 ) can be interpreted in terms of the ability of genes to absorb the effects of the inhibition of other correlated genes. Stated differently, we show that the Shapley value highlights the role of genes in the overall “connectivity” of a co-expression network, by taking into account the effect that their removal has over the induced sub-networks.…”

“…The more the genes that are directly interacting in the network with genes in the coalition, and therefore the ability of the coalition to keep the network connected, the higher the strength of the coalition. Following the approach introduced in the paper (Cesari et al 2017 ), we propose the Shapley value of such a coalitional game as a relevance index for genes in co-expression networks, taking into account the marginal contributions of genes to the connectivity of all the coalitions of genes in the network. We use the Shapley value to assess the relevance of genes in a real co-expression network related to lung cancer, by means of three different analyses.…”

“…In this paper, we apply a game theoretic index recently introduced in the paper (Cesari et al 2017 ) to identify the most relevant genes in a co-expression network. Such an index generalizes the notion of degree centrality, whose correlation with the essential genes for different biological systems is supported by several studies (see Bergmann et al (2004) , Carlson et al (2006) , Jeong et al (2001) , Junker et al (2006) , Zampetaki et al (2010 )).…”

“…Then, we use the Shapley value ( Shapley 1953 ) of a cooperative game to quantify the potential of a gene in preserving the regulatory activity across all possible subsets of genes in a co-expression network. In the paper (Cesari et al 2017 ) we used the axiomatic approach in order to justify the use of the Shapley value as a centrality measure, i.e., we proved that the Shapley value is the unique index that satisfy a set of properties with a precise meaning in the context of co-expression networks. In this paper, our objective is to show that the ability of the Shapley value to single out relevant genes in a co-expression network from the literature, is comparable to the one of other classical centrality measures.…”

“…At the same time, we show that the information provided in terms of genes selected by the Shapley value is complementary to the information provided by the other measures. In other words, this paper is devoted to the application and the validation of the relevance index introduced in the paper ( Cesari et al 2017 ), and its comparison with other classical centrality indices.…”