The Grand Canonical ensemble of weighted networks

Abstract

The cornerstone of statistical mechanics of complex networks is the idea that the links, and not the nodes, are the effective particles of the system. Here we formulate a mapping between weighted networks and lattice gasses, making the conceptual step forward of interpreting weighted links as particles with a generalised coordinate. This leads to the definition of the grand canonical ensemble of weighted complex networks. We derive exact expressions for the partition function and thermodynamic quantities, both in the cases of global and local (i.e., node-specific) constraints on density and mean energy of particles. We further show that, when modelling real cases of networks, the binary and weighted statistics of the ensemble can be disentangled, leading to a simplified framework for a range of practical applications.

References in corpus (21)

• The architecture of complex weighted networks
• Bose-Einstein condensation in complex networks
• The statistical mechanics of networks
• Line Graphs, Link Partitions and Overlapping Communities
• The Statistical Physics of Real-World Networks
• Statistical Mechanics of Multiplex Ensembles: Entropy and Overlap
• The entropy of randomized network ensembles
• Analytical maximum-likelihood method to detect patterns in real networks
• Generalized Bose-Fermi statistics and structural correlations in weighted networks
• Statistical Inference for Valued-Edge Networks: Generalized Exponential Random Graph Models
• Enhanced reconstruction of weighted networks from strengths and degrees
• Reconstruction methods for networks: the case of economic and financial systems
• Principles of statistical mechanics of random networks
• Statistical mechanics of topological phase transitions in networks
• Homogeneous complex networks
• Multi-species grandcanonical models for networks with reciprocity
• Estimating topological properties of weighted networks from limited information
• A GDP-driven model for the binary and weighted structure of the International Trade Network
• Social Stability and Extended Social Balance - Quantifying the Role of Inactive Links in Social Networks
• Statistical Mechanics of Multi-Edge Networks
• The role of adjacency matrix degeneration in maximum entropy weighted network models

Cited by in corpus (16)

• The Physics of Financial Networks
• Fast and scalable likelihood maximization for Exponential Random Graph Models with local constraints
• Does the brain behave like a (complex) network? I. Dynamics
• Reconstructing networks
• A faster horse on a safer trail: generalized inference for the efficient reconstruction of weighted networks
• Meta-validation of bipartite network projections
• Centrality anomalies in complex networks as a result of model over-simplification
• Bow-Tie Structures of Twitter Discursive Communities
• Weighted hypersoft configuration model
• Maximum Entropy approach to multivariate time series randomization
• Grand canonical ensembles of sparse networks and Bayesian inference
• Controlling network ensembles
• Generalized Markov stability of network communities
• Maximum entropy modeling of Optimal Transport: the sub-optimality regime and the transition from dense to sparse networks
• Gravity models of networks: integrating maximum-entropy and econometric approaches
• Approximate Conditional Sampling for Pattern Detection in Weighted Networks