Abstract
The spectral densities, or the density of states, of several types of
matrices associated with random complex networks are studied.
Non-linear functional equations for the spectral densities are
derived for the weighted Laplacian, random walk and weighted adjacency
matrices using the replica method on the static model.
Focusing on the scale-free networks with degree exponent
$łambda$ and on the case where the link weights are
parametrized by a weight exponent $\beta$,
explicit exact results are obtained
in the limit of large mean degree after the thermodynamic limit,
for arbitrary $łambda$ and $\beta$.
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