Griffiths phase on hierarchical modular networks with small-world edges

• Authors: Shanshan Li, Emory University
• Journal Title: Physical Review E
• Volume: Volume 95, Number 3
• Publisher: American Physical Society | 2017-03-06, Pages 032306-032306
• Type of Work: Article | Final Publisher PDF
• Publisher DOI: http://doi.org/10.1103/PhysRevE.95.032306
• Subjects: Physics, General
• Keywords: hierarchical modular networks; Griffiths phase

Abstract

The Griffiths phase has been proposed to induce a stretched critical regime that facilitates self-organizing of brain networks for optimal function. This phase stems from the intrinsic structural heterogeneity of brain networks, i.e., the hierarchical modular structure. In this work, the Griffiths phase is studied in modified hierarchical networks with small-world connections based on the 3-regular Hanoi network. Through extensive simulations, the hierarchical level-dependent inter-module wiring probabilities are identified to determine the emergence of the Griffiths phase. Numerical results and the complementary spectral analysis of the relevant networks can be helpful for a deeper understanding of the essential structural characteristics of finite-dimensional networks to support the Griffiths phase.