Scaling relation for earthquake networks

TL;DR

This paper demonstrates that a theoretical scaling relation between connectivity and eigenvalue distributions holds true for earthquake networks derived from seismic data, revealing insights into their hierarchical structure.

Contribution

It verifies the scaling relation in real earthquake networks, extending its applicability beyond theoretical models to seismic data.

Findings

The scaling relation holds well for earthquake networks from California and Japan.

Earthquake networks exhibit hierarchical organization consistent with the scaling relation.

The relation provides insight into the network structure of seismic activity.

Abstract

The scaling relation derived by Dorogovtsev, Goltsev, Mendes and Samukhin [Phys. Rev. E, 68 (2003) 046109] states that the exponents of the power-law connectivity distribution, gamma, and the power-law eigenvalue distribution of the adjacency matrix, delta, of a locally treelike scale-free network satisfy 2*gamma - delta = 1 in the mean field approximation. Here, it is shown that this relation holds well for the reduced simple earthquake networks (without tadpole-loops and multiple edges) constructed from the seismic data taken from California and Japan. The result is interpreted from the viewpoint of the hierarchical organization of the earthquake networks.