In this paper, we analyze the limiting spectral distribution of the adjacency
matrix of a random graph ensemble, proposed by Chung and Lu, in which a given
expected degree sequence wnT=(w1(n),…,wn(n))
is prescribed on the ensemble. Let ai,j=1 if there is an edge
between the nodes {i,j} and zero otherwise, and consider the normalized
random adjacency matrix of the graph ensemble: An=[ai,j/n]i,j=1n. The empirical spectral distribution
of An denoted by Fn(⋅) is the empirical
measure putting a mass 1/n at each of the n real eigenvalues of the
symmetric matrix An. Under some technical conditions on the
expected degree sequence, we show that with probability one,
Fn(⋅) converges weakly to a deterministic
distribution F(⋅). Furthermore, we fully characterize this
distribution by providing explicit expressions for the moments of
F(⋅). We apply our results to well-known degree distributions,
such as power-law and exponential. The asymptotic expressions of the spectral
moments in each case provide significant insights about the bulk behavior of
the eigenvalue spectrum