The diameter of Inhomogeneous random graphs

In this paper we study the diameter of Inhomogeneous random graphs $G(n,κ,p)$ that are induced by irreducible kernels $κ$. The kernels we consider act on separable metric spaces and are almost everywhere continuous. We generalize results known for the Erdős-Rényi model $G(n,p)$ for several ranges of $p$. We find upper and lower bounds for the diameter of $G(n,κ,p)$ in terms of the expansion factor and two explicit constants that depend on the behavior of the kernel over partitions of the metric space.

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