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Generation of arbitrarily two-point-correlated random networks
Sebastian Weber1, Markus Porto
1Institut für Festkörperphysik, Technische Universität Darmstadt, Hochschulstrasse 8, 64289 Darmstadt, Germany.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 13, 2007
Summary
Researchers developed an efficient algorithm to generate complex random networks with specific degree correlations. This method allows simultaneous control over degree distribution and average nearest neighbor function for network analysis.
Area of Science:
- Network Science
- Statistical Physics
- Computer Science
Background:
- Random networks serve as crucial null models for understanding complex systems.
- Investigating network properties requires accurate generation of correlated random networks.
Purpose of the Study:
- To present an efficient algorithm for generating undirected random networks with specified two-point degree-degree correlations.
- To develop a formalism for constructing joint degree distributions to control network properties simultaneously.
- To generalize the algorithm for annealed networks, enabling mean-field analysis.
Main Methods:
- An efficient and accurate algorithm for generating random networks with arbitrary two-point degree-degree correlations.
- A formalism to construct a joint degree distribution P(j,k) to fix P(k) and k_nn(k) simultaneously.
- Generalization of the algorithm to annealed networks.
Main Results:
- The algorithm successfully generates random networks without self-edges or multiple edges.
- Demonstrated the formalism with scale-free and empirical complex networks.
- The method allows simultaneous control over degree distribution and average nearest neighbor function.
Conclusions:
- The developed algorithm and formalism provide a powerful tool for studying the influence of degree correlations in complex networks.
- The generalization to annealed networks offers a mean-field perspective on network structures.
- Enables systematic investigation of network properties by precisely controlling correlations.
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