Generalized Bose-Fermi statistics and structural correlations in weighted networks.

We derive a class of generalized statistics, unifying the Bose and Fermi ones, that describe any system where the first-occupation energies or probabilities are different from subsequent ones, as in the presence of thresholds, saturation, or aging. The statistics completely describe the structural correlations of weighted networks, which turn out to be stronger than expected and to determine significant topological biases. Our results show that the null behavior of weighted networks is different from what was previously believed, and that a systematic redefinition of weighted properties is necessary.