Connectivity of inhomogeneous random graphs

We find conditions for the connectivity of inhomogeneous random graphs with intermediate density. Our results generalize the classical result for G ( n, p ), when . We draw n independent points X i from a general distribution on a separable metric space, and let their indices form the vertex set of a graph. An edge ( i, j ) is added with probability , where is a fixed kernel. We show that, under reasonably weak assumptions, the connectivity threshold of the model can be determined.