  The eigenvalues and eigenvectors of the connectivity matrix of complex
networks contain information about its topology and its collective behavior. In
particular, the spectral density $\rho(\lambda)$ of this matrix reveals
important network characteristics: random networks follow Wigner's semicircular
law whereas scale-free networks exhibit a triangular distribution. In this
paper we show that the spectral density of hierarchical networks follow a very
different pattern, which can be used as a fingerprint of modularity. Of
particular importance is the value $\rho(0)$, related to the homeostatic
response of the network: it is maximum for random and scale free networks but
very small for hierarchical modular networks. It is also large for an actual
biological protein-protein interaction network, demonstrating that the current
leading model for such networks is not adequate.
