Griffiths phase on hierarchical modular networks with small-world edges

Area of Science:

• Neuroscience
• Network Science
• Complex Systems

Background:

• The Griffiths phase is theorized to create a critical state in brain networks, enabling self-organization for optimal function.
• This critical state arises from the inherent structural complexity of brain networks, specifically their hierarchical modular organization.

Purpose of the Study:

• To investigate the emergence of the Griffiths phase in modified hierarchical networks with small-world connections.
• To identify the specific network properties that govern the presence of the Griffiths phase.

Main Methods:

• Utilized simulations on modified hierarchical networks based on the 3-regular Hanoi network.
• Employed spectral analysis to complement numerical findings.

Main Results:

• Identified hierarchical level-dependent inter-module wiring probabilities as key determinants for the Griffiths phase.
• Demonstrated the influence of network structure on the emergence of this critical regime.

Conclusions:

• The study elucidates the structural characteristics necessary for supporting the Griffiths phase in finite networks.
• Findings contribute to understanding how network heterogeneity facilitates optimal brain function through self-organization.