Connectivity of inhomogeneous random graphs (Q2930053)

This paper studies connectivity of inhomogeneous random graphs with intermediate density. Given a separable metric space \(S\) and a Borel probability measure \(\mu\), the random graph has vertex set \([n]\) and edge set \(\{(i,j)\}\) with each pair \((i,j)\) appearing with probability \(\min\{1,\kappa(X_i,X_j)\log n/n\}\). Here, the \(X_i\)s are independent \(\mu\)-distributed random variables on \(S\), and \(\kappa\in L^1(S\times S,\mu\otimes\mu)\) is a non-negative symmetric integrable kernel. The connectivity threshold of the model is presented under some conditions.