The size of the largest component below phase transition in inhomogeneous random graphs

Abstract

We study the "rank 1 case" of the inhomogeneous random graph model. In the subcritical case we derive an exact formula for the asymptotic size of the largest connected component scaled to log n. This result is new, it completes the corresponding known result in the supercritical case. We provide some examples of application of a new formula.

23 pages

References in corpus (1)

• Merging percolation on $Z^d$ and classical random graphs: Phase transition

Cited by in corpus (2)

• Diffusion approximation for the components in critical inhomogeneous random graphs of rank 1
• Asymptotics for the size of the largest component scaled to "log n" in inhomogeneous random graphs