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Tailored graph ensembles as proxies or null models for real networks I: tools for quantifying structure
A Annibale1, Acc Coolen, Lp Fernandes
1Department of Mathematics, King's College London, The Strand, London WC2R 2LS, United Kingdom.
Journal of Physics A: Mathematical and General
|September 17, 2010
Summary
This study introduces tailored random graph ensembles for analyzing real networks. These ensembles provide mathematical tools to quantify and compare network structures beyond simple degree statistics.
Area of Science:
- Network science
- Statistical physics
- Graph theory
Background:
- Real-world networks exhibit complex topological properties.
- Existing methods for network analysis often rely on limited statistics, such as degree distributions.
- A gap exists in macroscopic tools for comparing network structures beyond basic properties.
Purpose of the Study:
- To develop tailored random graph ensembles for modeling real networks.
- To create precise mathematical tools for macroscopic network topology quantification and comparison.
- To extend network analysis beyond simple degree statistics.
Main Methods:
- Construction of a family of structured random graph ensembles.
- Analytical calculation of control parameters for the ensembles.
- Derivation of asymptotic formulae for network properties.
Main Results:
- The proposed ensembles can generate graphs with any specified degree distribution and degree-degree correlation.
- Control parameters for the ensembles are fully calculable analytically.
- Asymptotic formulae for network entropies, complexities, and information-theoretic distances are derived.
Conclusions:
- The developed framework offers a powerful method for macroscopic network analysis.
- This approach enables direct comparison of network topologies based on degree distribution and correlations.
- The mathematical tools provide precise and practical insights into network structures.
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