  We study numerically and analytically the spectrum of incidence matrices of
random labeled graphs on N vertices : any pair of vertices is connected by an
edge with probability p. We give two algorithms to compute the moments of the
eigenvalue distribution as explicit polynomials in N and p. For large N and
fixed p the spectrum contains a large eigenvalue at Np and a semi-circle of
"small" eigenvalues. For large N and fixed average connectivity pN (dilute or
sparse random matrices limit), we show that the spectrum always contains a
discrete component. An anomaly in the spectrum near eigenvalue 0 for
connectivity close to e=2.72... is observed. We develop recursion relations to
compute the moments as explicit polynomials in pN. Their growth is slow enough
so that they determine the spectrum. The extension of our methods to the
Laplacian matrix is given in Appendix.
  Keywords: random graphs, random matrices, sparse matrices, incidence matrices
spectrum, moments
