Organization in complex brain networks: Energy distributions and phase shift

Area of Science:

• Network science
• Computational neuroscience
• Statistical physics

Background:

• The Hamiltonian function quantifies energy distribution within complex networks.
• Brain networks exhibit hierarchical structures and power-law distributions, suggesting self-organization.

Purpose of the Study:

• To investigate the role of the Hamiltonian function and a resolution parameter in brain network energy distribution.
• To explore the relationship between network energy, self-organization, and brain states.

Main Methods:

• Analysis of network Hamiltonian functions derived from node and edge distributions.
• Investigation of network properties modulated by a resolution parameter.
• Identification of phase transitions in network behavior as a function of the resolution parameter.

Main Results:

• The Hamiltonian function in brain networks displays hierarchical features consistent with power-law behavior.
• Three distinct phases of network behavior were observed, driven by the resolution parameter.
• The resolution parameter influences energy distribution and may indicate different brain states.

Conclusions:

• The Hamiltonian function provides insights into energy distribution and self-organization in brain networks.
• The resolution parameter appears to be a critical factor controlling network energy balance and potentially brain states.
• This framework offers a novel perspective on understanding brain dynamics and organization.