Law of large numbers for the largest component in a hyperbolic model of complex networks

Understand

We consider the component structure of a recent model of random graphs on the hyperbolic plane that was introduced by Krioukov et al.

• The model exhibits a power law degree sequence, small distances and clustering, features that are associated with the so-called complex networks.
• The model is controlled by two parameters $\alpha$ and $\nu$ where, roughly speaking, $\alpha$ controls the exponent of the power law and $\nu$ controls the average degree.
• Refining earlier results, we are able to show a law of large numbers for the largest component.