Correlations in random Apollonian network

Details Correlations in random Apollonian network Correlations in random Apollonian network

2006-09-12

arxiv.org/abs/cond-mat/0609270v2

Physica A 380 (2007) 621-628

Physics

Condensed Matter

Statistical Mechanics

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

Scientific paper

10.1016/j.physa.2007.02.058

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.

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