J. Hladký

Connectivity of Inhomogeneous Random Graphs II

Each graphon W:Ω2→[0,1]$$ W:{\Omega}^2\to \left[0,1\right] $$ yields an inhomogeneous random graph model 𝔾(n,W) . We show that 𝔾(n,W) is asymptotically almost surely connected if and only if (i) W$$ W $$ is a connected graphon and (ii) the measure of elements of Ω$$ \Omega $$ of W$$ W $$ ‐degree less than α$$ \alpha $$...