entropy maximizing distribution with absolute power constraint

Holland, P.W., Leinhardt, S.: An exponential family of probability distributions for directed graphs. Squartini, T., Garlaschelli, D.: Analytical maximum-likelihood method to detect patterns in real networks. Garlaschelli, D., Loffredo, M.: Maximum likelihood: extracting unbiased information from complex networks. doi: 10.1103/PhysRevE.70.066117īianconi, G.: The entropy of randomized network ensembles. Park, J., Newman, M.E.J.: Statistical mechanics of networks. doi: 10.1007/PL00012580Ĭhung, F., Linyuan, L.: The average distances in random graphs with given expected degrees. doi: 10.1103/PhysRevE.64.025102Ĭhung, F., Linyuan, L.: Connected components in random graphs with given expected degree sequences. Newman, M.E.J.: Clustering and preferential attachment in growing networks. Algorithm 6, 161–179 (1995)ĭhamdhere, A., Dovrolis, C.: Twelve years in the evolution of the internet ecosystem. Molloy, M., Reed, B.: A critical point for random graphs with a given degree sequence. 6, 290–297 (1959)īender, E.A., Canfield, E.R.: The asymptotic number of labeled graphs with given degree sequences. Solomonoff, R., Rapoport, A.: Connectivity of random nets. Cambridge University Press, Cambridge (2016) Oxford University Press, Oxford (2010)īarabási, A.-L.: Network Science. Newman, M.E.J.: Networks: An Introduction. The proof of their unbiasedness relies on generalized graphons, and on mapping the problem of maximization of the normalized Gibbs entropy of a random graph ensemble, to the graphon entropy maximization problem, showing that the two entropies converge to each other in the large-graph limit.īoccaletti, S., Latora, V., Moreno, Y., Chavez, M., Hwanga, D.-U.: Complex networks: structure and dynamics. Here we prove that the hypersoft configuration model, belonging to the class of random graphs with latent hyperparameters, also known as inhomogeneous random graphs or W-random graphs, is an ensemble of random power-law graphs that are sparse, unbiased, and either exchangeable or projective. The last requirement states that entropy of the graph ensemble must be maximized under the degree distribution constraints. These requirements are: sparsity, exchangeability, projectivity, and unbiasedness. Even though power-law or close-to-power-law degree distributions are ubiquitously observed in a great variety of large real networks, the mathematically satisfactory treatment of random power-law graphs satisfying basic statistical requirements of realism is still lacking.

Entropy maximizing distribution with absolute power constraint