Let A(G) be the adjacency matrix of a graph G with λ1(G), λ2(G), . . . , λn(G) its eigenvalues in non-increasing order. Call the number Sk(G) := ∑ n i=1 λ i (G) (k = 0, 1, . . . , n − 1) the kth spectral moment of G. Let S(G) = (S0(G), S1(G), . . . , Sn−1(G)) be the sequence of spectral moments of G. For two graphsG1 and G2, we have G1 ≺s G2 if Si(G1) = Si(G2) for i = 0, 1, . . . , k−1 and Sk(G...

Let A(G) be the adjacency matrix of a graph G with λ1(G), λ2(G), . . . , λn(G) its eigenvalues in non-increasing order. Call the number Sk(G) := ∑ n i=1 λ i (G) (k = 0, 1, . . . , n − 1) the kth spectral moment of G. Let S(G) = (S0(G), S1(G), . . . , Sn−1(G)) be the sequence of spectral moments of G. For two graphsG1 and G2, we have G1 ≺s G2 if Si(G1) = Si(G2) for i = 0, 1, . . . , k−1 and Sk(G...

We compute an asymptotic expansion with precision 1/n of the moments of the expected empirical spectral measure of Wigner matrices of size n with independent centered entries. We interpret this expansion as the moments of the addition of the semicircle law and 1/n times an explicit signed measured with null total mass. This signed measure depends only on the second and fourth moments of the ent...