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 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 previously believed, and that a systematic redefinition of weighted properties is necessary.

💡 Research Summary

The paper introduces a unified statistical framework that bridges Bose‑Einstein (BE) and Fermi‑Dirac (FD) statistics by allowing the energy (or probability) associated with the first occupation of a state to differ from that of subsequent occupations. This “generalized Bose‑Fermi statistics” is defined through two parameters: ε₁ for the first occupation and ε₂ for each additional occupation. The probability of a state being occupied k times is proportional to exp