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Combinatorial study of degree assortativity in networks
1Department of Mathematics and Statistics, SUPA and Institute of Complex Systems, University of Strathclyde, Glasgow G1 1XQ, United Kingdom.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 21, 2011
Summary
Network assortativity, whether a network is assortative or disassortative, is determined by three factors: transitivity, intermodular connectivity, and branching. Highly branched networks tend to be disassortative.
Area of Science:
- Network Science
- Graph Theory
- Statistical Physics
Background:
- Real-world networks exhibit diverse degree-degree correlations, ranging from assortative to disassortative patterns.
- Understanding the underlying structural determinants of these correlations is crucial for network analysis.
Purpose of the Study:
- To mathematically prove the key structural factors governing network assortativity.
- To establish a predictive framework for network degree-degree correlation based on network topology.
Main Methods:
- Combinatorial methods were employed to analyze network structures.
- The study focused on three specific structural properties: transitivity (clustering coefficient), intermodular connectivity, and branching.
Main Results:
- Network assortativity is proven to depend solely on transitivity, intermodular connectivity, and branching.
- A network is assortative when the combined influence of transitivity and intermodular connectivity outweighs that of branching.
- Highly branched network structures are predominantly disassortative.
Conclusions:
- The study provides a combinatorial proof for the factors determining network assortativity.
- Network branching emerges as a critical factor driving disassortative behavior in many real-world networks.
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