  In 2002, Chung and Lu introduced a version of the Erdos-Renyi model which an
edge between $i$ and $j$ is present with probability $p(i,j)$. They applied
this model to compute the diameter of power-law random graphs, with yielded
easier proofs than those for the configuration model. In 2007 their model was
brought and integrated under the umbrella of Bolobas, Janson, and Riordan's
inhomogeneous random graphs. However, the properties of the Chung-Lu model were
never fully explored. In this paper, we fill the gap by giving a result for the
cluster sizes in the subcritical regime and the fraction of vertices in the
giant component in the supercritical phase.
