Abstract:
Empirical bipartite networks are analyzed by spectral methods. We show that their properties are very different from common random-matrix models. Most importantly, we show that the density of eigenvalues has a power-law tail without band edge. We compare the spectra of the real network with reshuffled network with conserved degrees and with matrix whose elements were randomly permuted. The former randomization preserves most properties but in the latter all special features are lost. Similar comparislon is made for the localization properties. The original network does not exhibit a localization threshold, but the localised eigenvectors are mixed with the extended ones. The most localised eigenvectors reveal very special details of the network. Level spacing analysis shows that the matrix encoding the network belongs to the universality class of Gaussian unitary ensemble.