Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral Analysis and the Dynamic Response of Complex Networks   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.

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The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an