Y. Shang
Lack of Gromov-hyperbolicity in colored random networks
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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.