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Solution for the properties of a clustered network.

Juyong Park¹, M E J Newman

¹Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1120, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|October 4, 2005

Summary

We analyzed Strauss

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Area of Science:

Network science
Statistical physics

Background:

Strauss's network model exhibits a degenerate region with unrealistically dense subgraphs.
Previous computational methods failed to fully analyze this region.

Purpose of the Study:

To provide an analytic mean-field solution for Strauss's network model.
To characterize the degenerate region and its associated phase transition.

Main Methods:

Developed an analytic mean-field solution.
Analyzed the model in the limit of large network size.

Main Results:

The degenerate region is identified as a symmetry-broken phase.
The onset of degeneracy corresponds to a first-order phase transition in network density.

Conclusions:

The analytic solution accurately describes the network model's behavior.
Provides a theoretical understanding of dense subgraph formation and phase transitions in clustered networks.

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