Large deviation and anomalous fluctuations scaling in degree assortativity on configuration networks

Abstract

By constructing a multicanonical Monte Carlo simulation, we obtain the full probability distribution ${\rho }_N(r)$ of the degree assortativity coefficient $r$ on configuration networks of size $N$ by using the multiple histogram reweighting method. We suggest that ${\rho }_N(r)$ obeys a large deviation principle, ${\rho }_N\left(r-r_N^{\ast }\right)\asymp e^{-N^{\xi }I\left(r-r_N^{\ast }\right)}$, where the rate function $I$ is convex and possesses its unique minimum at $r=r_N^{\ast }$, and $\xi$ is an exponent that scales ${\rho }_N$'s with $N$. We show that $\xi =1$ for Poisson random graphs, and $\xi \ge 1$ for scale-free networks in which $\xi$ is a decreasing function of the degree distribution exponent $\gamma$. Our results reveal that the fluctuations of $r$ exhibits an anomalous scaling with $N$ in highly heterogeneous networks.

arXiv comment9 pages, 9 figures

References in corpus (69)

• The structure and function of complex networks
• Assortative mixing in networks
• Statistical physics of social dynamics
• Epidemic processes in complex networks
• Random graphs with arbitrary degree distributions and their applications
• Synchronization in complex networks
• Mixing patterns in networks
• Specificity and stability in topology of protein networks
• An efficient, multiple range random walk algorithm to calculate the density of states
• Critical phenomena in complex networks
• The large deviation approach to statistical mechanics
• Statistical physics of human cooperation
• The Kuramoto model in complex networks
• The statistical mechanics of networks
• Control Principles of Complex Networks
• Epidemic spreading in correlated complex networks
• Absence of epidemic threshold in scale-free networks with connectivity correlations
• The Statistical Physics of Real-World Networks
• Entropy measures for complex networks: Toward an information theory of complex topologies
• Statistical Mechanics of Multiplex Ensembles: Entropy and Overlap
• Explosive transitions in complex networks' structure and dynamics: percolation and synchronization
• Pattern Detection in Complex Networks: Correlation Profile of the Internet
• Epidemic threshold in structured scale-free networks
• Generating simple random graphs with prescribed degree distribution
• Resilience to damage of graphs with degree correlations
• Construction and properties of assortative random networks
• The origin of degree correlations in the Internet and other networks
• Assortativity Decreases the Robustness of Interdependent Networks
• Generalized network structures: The configuration model and the canonical ensemble of simplicial complexes
• Analytical maximum-likelihood method to detect patterns in real networks
• Large Deviations in Single File Diffusion
• The entropic origin of disassortativity in complex networks
• Gibbs entropy of networks ensembles by cavity methods
• Uncovering disassortativity in large scale-free networks
• Degree-degree correlations in random graphs with heavy-tailed degrees
• Large-deviation properties of largest component for random graphs
• Synchronization in weighed scale-free networks with degree-degree correlation
• Epidemic extinction and control in heterogeneous networks
• Large deviations for the height in 1D Kardar-Parisi-Zhang growth at late times
• Zero Pearson Coefficient for Strongly Correlated Growing Trees
• Rare events and discontinuous percolation transitions
• Large deviations of surface height in the $1+1$-dimensional Kardar-Parisi-Zhang equation: exact long-time results for $\lambda H<0$
• Anomalous scaling of dynamical large deviations
• Constrained Markovian dynamics of random graphs
• Coulomb-gas electrostatics controls large fluctuations of the KPZ equation
• Large-deviation properties of the largest biconnected component for random graphs
• Distribution of diameters for Erdös-Rényi random graphs
• Entropy distribution and condensation in random networks with a given degree distribution
• Large deviation theory of percolation on multiplex networks
• Large-deviation properties of resilience of power grids
• Large deviations of random walks on random graphs
• Sampling motif-constrained ensembles of networks
• Measuring degree-degree association in networks
• Multicanonical MCMC for Sampling Rare Events
• Bias in generation of random graphs
• Epidemic Extinction Paths in Complex Networks
• Large-deviation properties of resilience of transportation networks
• Response of degree-correlated scale-free networks to stimuli
• Generalized optimal paths and weight distributions revealed through the large deviations of random walks on networks
• Lower bound of assortativity coefficient in scale-free networks
• Probability of graphs with large spectral gap by multicanonical Monte Carlo
• Degree Dispersion Increases the Rate of Rare Events in Population Networks
• Large deviation induced phase switch in an inertial majority-vote model
• Dynamical phase transition to localized states in the two-dimensional random walk conditioned on partial currents
• Condensation of degrees emerging through a first-order phase transition in classical random graphs
• Importance Sampling of Rare Events in Chaotic Systems
• Analytic solution of the two-star model with correlated degrees
• Taming chaos to sample rare events: the effect of weak chaos
• Random degree-degree correlated networks

Cited by in corpus (2)

• Generalized optimal paths and weight distributions revealed through the large deviations of random walks on networks
• Analytic solution of the two-star model with correlated degrees