Number of loops of size h in growing scale-free networks

Abstract

The hierarchical structure of scale-free networks has been investigated focusing on the scaling of the number $N_h(t)$ of loops of size h as a function of the system size. In particular we have found the analytic expression for the scaling of $N_h(t)$ in the Barabási-Albert (BA) scale-free network. We have performed numerical simulations on the scaling law for $N_h(t)$ in the BA network and in other growing scale free networks, such as the bosonic network (BN) and the aging nodes (AN) network. We show that in the bosonic network and in the aging node network the phase transitions in the topology of the network are accompained by a change in the scaling of the number of loops with the system size.

arXiv comment4 pages, 3 figures

References in corpus (16)

• Emergence of scaling in random networks
• Statistical mechanics of complex networks
• Epidemic spreading in scale-free networks
• Lethality and centrality in protein networks
• Evolution of networks
• Resilience of the Internet to random breakdowns
• Mean-field theory for scale-free random networks
• Breakdown of the Internet under intentional attack
• Bose-Einstein condensation in complex networks
• Evolution of reference networks with aging
• Ising Model on Networks with an Arbitrary Distribution of Connections
• Growing Scale-Free Networks with Small World Behavior
• Scaling properties of scale-free evolving networks: Continuous approach
• Ferromagnetic ordering in graphs with arbitrary degree distribution
• Ferromagnetic Phase Transition in Barabasi-Albert Networks
• Mean field solution of the Ising model on a Barabasi-Albert network

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