A Self-Adaptive Centrality Measure for Asset Correlation Networks

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.

Keywords

• epidemic models
• centrality measures
• eigenvector centrality
• nonlinear eigenproblem