Correlations in random Apollonian network

Abstract

In this paper, by both simulations and theoretical predictions we study two and three node (or degree) correlations in random Apollonian network (RAN), which have small-world and scale-free topologies. Using the rate equation approach under the assumption of continuous degree, we first give the analytical solution for two node correlations, expressed by average nearest-neighbor degree (ANND). Then, we revisit the degree distribution of RAN using rate equation method and get the exact connection distribution, based on which we derive a more accurate result for mean clustering coefficient as an average quantity of three degree correlations than the one previously reported. Analytical results reveal that ANND has no correlations with respect to degree, while clustering coefficient is dependent on degree, showing a power-law behavior as $C(k)\sim k^{-1}$. The obtained expressions are successfully contrasted with extensive numerical simulations.

11 pages, 3 figures. Accepted for publication in Physica A

References in corpus (5)

• Self-similar disk packings as model spatial scale-free networks
• A deterministic small-world network created by edge iterations
• Recursive graphs with small-world scale-free properties
• Characterizing the network topology of the energy landscapes of atomic clusters
• Distance-d covering problems in scale-free networks with degree correlations

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