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Gibbs entropy of network ensembles by cavity methods
Kartik Anand1, Ginestra Bianconi
1Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34014 Trieste, Italy.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 28, 2010
Summary
We reveal how Gibbs entropy in network ensembles connects to large deviations in related canonical ensembles. This provides a new way to understand order and randomness in real-world networks.
Area of Science:
- Statistical mechanics
- Network science
- Information theory
Background:
- Gibbs entropy quantifies order/randomness in network configurations under constraints.
- Understanding network structure is crucial in various scientific fields.
Purpose of the Study:
- To establish a formal connection between Gibbs entropy of microcanonical network ensembles and large deviations of conjugated canonical ensembles.
- To provide exact expressions for this relationship using cavity methods.
Main Methods:
- Utilized cavity methods from statistical physics.
- Applied the methods to specific network models: configuration model, ensembles with constrained degree sequences, and community structures.
- Derived exact expressions for the entropy-canonical ensemble correspondence.
Main Results:
- Established an exact relationship between microcanonical Gibbs entropy and large deviations in canonical ensembles for several network models.
- Demonstrated the utility of cavity methods for analyzing constrained network ensembles.
Conclusions:
- The derived correspondence offers a novel perspective on network entropy and its relation to statistical mechanics.
- The findings facilitate a deeper understanding of the statistical properties and emergent behaviors of complex networks.
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