Evolving networks by merging cliques

Abstract

We propose a model for evolving networks by merging building blocks represented as complete graphs, reminiscent of modules in biological system or communities in sociology. The model shows power-law degree distributions, power-law clustering spectra and high average clustering coefficients independent of network size. The analytical solutions indicate that a degree exponent is determined by the ratio of the number of merging nodes to that of all nodes in the blocks, demonstrating that the exponent is tunable, and are also applicable when the blocks are classical networks such as Erdős-Rényi or regular graphs. Our model becomes the same model as the Barabási-Albert model under a specific condition.

8 pages, 8 figures

References in corpus (8)

• Hierarchical organization of modularity in metabolic networks
• Small-world properties of the Indian Railway network
• Weighted evolving networks: coupling topology and weights dynamics
• Growing networks with local rules: preferential attachment, clustering hierarchy and degree correlations
• Structural transitions in scale-free networks
• Rate equation approach for correlations in growing network models
• Mean-field theory for clustering coefficients in Barabasi-Albert networks
• Network Transitivity and Matrix Models

Cited by in corpus (10)

• Analyzing and Modeling Real-World Phenomena with Complex Networks: A Survey of Applications
• Clique Graphs and Overlapping Communities
• Structure of n-clique networks embedded in a complex network
• Tuning degree distributions of scale-free networks
• Local cause of coherence in Boolean networks
• Effects of feedback and feedforward loops on dynamics of transcriptional regulatory model networks
• Hybrid evolving clique-networks and their communicability
• Modeling Transitivity in Complex Networks
• General Connectivity Distribution Functions for Growing Networks with Preferential Attachment of Fractional Power
• Modeling for evolving biological networks with scale-free connectivity, hierarchical modularity, and disassortativity