A Self-Adaptive Centrality Measure for Asset Correlation Networks

Author:

Bartesaghi Paolo1ORCID,Clemente Gian Paolo2ORCID,Grassi Rosanna1ORCID

Affiliation:

1. Department of Statistics and Quantitative Methods, University of Milano-Bicocca, Via Bicocca degli Arcimboldi 8, 20126 Milan, Italy

2. Department of Mathematics for Economic, Financial and Actuarial Sciences, Università Cattolica del Sacro Cuore, Largo Gemelli 1, 20123 Milan, Italy

Abstract

We propose a new centrality measure based on a self-adaptive epidemic model characterized by an endogenous reinforcement mechanism in the transmission of information between nodes. We provide a strategy to assign to nodes a centrality score that depends, in an eigenvector centrality scheme, on that of all the elements of the network, nodes and edges, connected to it. We parameterize this score as a function of a reinforcement factor, which for the first time implements the intensity of the interaction between the network of nodes and that of the edges. In this proposal, a local centrality measure representing the steady state of a diffusion process incorporates the global information encoded in the whole network. This measure proves effective in identifying the most influential nodes in the propagation of rumors/shocks/behaviors in a social network. In the context of financial networks, it allows us to highlight strategic assets on correlation networks. The dependence on a coupling factor between graph and line graph also enables the different asset responses in terms of ranking, especially on scale-free networks obtained as minimum spanning trees from correlation networks.

Publisher

MDPI AG

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