Influence measures in subnetworks using vertex centrality
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Influence measures in subnetworks using vertex centrality Roy Cerqueti2 · Gian Paolo Clemente1 · Rosanna Grassi3
© Springer-Verlag GmbH Germany, part of Springer Nature 2019
Abstract This work deals with the issue of assessing the influence of a node in the entire network and in the subnetwork to which it belongs as well, adapting the classical idea of vertex centrality. We provide a general definition of relative vertex centrality measure with respect to the classical one, referred to the whole network. Specifically, we give a decomposition of the relative centrality measure by including also the relative influence of the single node with respect to a given subgraph containing it. The proposed measure of relative centrality is tested in the empirical networks generated by collecting assets of the S&P 100, focusing on two specific centrality indices: betweenness and eigenvector centrality. The analysis is performed in a time perspective, capturing the assets influence, with respect to the characteristics of the analysed measures, in both the entire network and the specific sectors to which the assets belong. Keywords Complex networks · Centrality measures · Correlation networks · Relative centrality
1 Introduction Complex networks are experiencing increasing popularity among scientists, either under a methodological as well as practical perspective. They represent a versatile framework for the description of real-world systems with interconnected components (see e.g. Newman 2010; Wasserman and Faust 1994). In the context of complex networks, a very relevant theme is the assessment of the relevance of the single nodes in the overall structure. In this respect, we mention, e.g. Cinelli et al (2017a), Cerqueti et al (2018), Ma and Ma (2019) Communicated by Philippe de Peretti.
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Rosanna Grassi [email protected] Roy Cerqueti [email protected] Gian Paolo Clemente [email protected]
1
Department of Mathematics for Economics, Financial and Actuarial Sciences, Universitá Cattolica del Sacro Cuore, Milan, Italy
2
Department of Economics and Law, University of Macerata, Via Crescimbeni 20, 62100 Macerata, Italy
3
Department of Statistics and Quantitative Methods, University of Milano-Bicocca, Via Bicocca degli Arcimboldi, 8, 20126 Milan, Italy
and Wang et al (2011), where the identification of the key actors among the agents is a crucial task for exploring the proposed applied problem—inter organizational innovation, social media and air transportation, respectively. Widely used instruments for identifying the influence of the single nodes in a complex network are the so-called centrality measures. Such devices compound a set of methodological tools sharing the same target of measuring the relevance of the nodes, with the distinctions due to the declination of the concept of relevance (see, e.g. Freeman and Freeman 1979; Perra and Fortunato 2008; Watts 2004). Centrality measures are usually defined as absolute quantities, hence providing an objective description of the importance of t
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