11-101 Y. Shang

Lack of Gromov-hyperbolicity in colored random networks (171K, PDF) Jun 28, 11

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Abstract. The geometry of complex networks has a close relationship with their structure and function. In this paper, we introduce an inhomogeneous random network $G(n,\{c_i\},\{p_i\})$, called the colored random network, and investigate its Gromov-hyperbolicity. We show that the colored random networks are non-hyperbolic in the regime $\sum_{i=1}^mc_i^2p_i=c/n$ for $c>1$, by approximation to binomial random graphs. Numerical simulations are provided to illustrate our results.

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