Non-Hyperbolicity of Random Graphs with Given Expected Degrees
Yilun Shang · Stochastic Models · 2013
The geometry of complex networks has a close relationship with their structure and function. In this article, we investigate Gromov-hyperbolicity of inhomogeneous random networks modeled by the Chung-Lu model G(w). When the maximum expected degree w max and minimum expected degree w min satisfy w max ≤ 21/3 w min, we prove that for any positive δ, G(w) has a positive probability of containing δ-fat triangles as n → ∞. Our numerical simulations illustrate this non-hyperbolicity of G(w) for power law degree distributions among others.