Network edge entropy decomposition with spin statistics

• Decompose the global thermodynamic entropy of a network into components associated with its edges. Calculate edge from partition functions classical and quantum statistics. Apply on synthetic real-world networks to evaluate qualitative quantitative differences in performance. In previous study, we have explored how decompose using graph-spectral decomposition technique. Here, develop this work more depth understand role as an efficient effective tool analysing structure. We use distribution feature or characterisation combine it linear discriminant analysis distinguish different types model Interpreting normalised Laplacian matrix Hamiltonian (or energy) operator, is assumed be equilibrium heat bath where energy states correspond eigenvalues. To way which particles occupy states, explore three spin-dependent statistical models determine network. These are a) spinless Maxwell-Boltzmann distribution, two based mechanical spin-statistics, namely b) Bose-Einstein for integer spin, c) Fermi-Dirac half-integer spin. By spectral Laplacian, illustrate project out edge-entropy entropy. way, detailed across edges can constructed. Compared our study von Neumann entropy, just depends degrees nodes forming edge, case new model, there subtle dependence structure used effectively identify variations structure, particular incorporating large degree. Numerical experiments data-sets presented