Fluctuation-dissipation relations in complex networks

Area of Science:

• Statistical physics
• Network science
• Complex systems

Background:

• Maximum-entropy random networks are fundamental models in network science.
• Understanding network susceptibility to external changes is crucial for analyzing real-world systems.
• Fluctuation-dissipation relations link microscopic properties to macroscopic responses.

Purpose of the Study:

• To investigate fluctuations in various maximum-entropy random network ensembles.
• To derive fluctuation-dissipation relations for network susceptibilities.
• To explore the origins of scale-free topologies in real-world networks.

Main Methods:

• Analysis of fluctuations across different network ensembles.
• Derivation of generalized fluctuation-dissipation relations.
• Investigation of networks with specified degree sequences and two-point correlations.

Main Results:

• Several fluctuation-dissipation relations were derived, quantifying network responses to external fields.
• Scale-free network topologies may result from self-organization towards low susceptibility.
• Equivalence was shown between networks with given degree sequences/two-point correlations and random networks with hidden variables.

Conclusions:

• The study provides theoretical insights into network stability and self-organization.
• Fluctuation-dissipation relations offer a framework for understanding network dynamics.
• The findings contribute to explaining the prevalence of scale-free structures in complex systems.