Generation of arbitrarily two-point correlated random networks

Abstract

Random networks are intensively used as null models to investigate properties of complex networks. We describe an efficient and accurate algorithm to generate arbitrarily two-point correlated undirected random networks without self- or multiple-edges among vertices. With the goal to systematically investigate the influence of two-point correlations, we furthermore develop a formalism to construct a joint degree distribution $P(j,k)$ which allows to fix an arbitrary degree distribution $P(k)$ and an arbitrary average nearest neighbor function $\knn(k)$ simultaneously. Using the presented algorithm, this formalism is demonstrated with scale-free networks ($P(k)\propto k^{-\gamma }$) and empirical complex networks ($P(k)$ taken from network) as examples. Finally, we generalize our algorithm to annealed networks which allows networks to be represented in a mean-field like manner.

10 pages, 6 figures

References in corpus (25)

• Emergence of scaling in random networks
• Statistical mechanics of complex networks
• The structure and function of complex networks
• Lethality and centrality in protein networks
• Assortative mixing in networks
• The diameter of the world wide web
• Evolution of networks
• Mixing patterns in networks
• Resilience of the Internet to random breakdowns
• Generation of uncorrelated random scale-free networks
• Origins of fractality in the growth of complex networks
• Properties of highly clustered networks
• Class of correlated random networks with hidden variables
• Ising Model on Networks with an Arbitrary Distribution of Connections
• Cut-offs and finite size effects in scale-free networks
• Statistical ensemble of scale-free random graphs
• Tuning clustering in random networks with arbitrary degree distributions
• Diffusion-annihilation processes in complex networks
• Metric structure of random networks
• Closing probabilities in the Kauffman model: an annealed computation
• Computational complexity arising from degree correlations in networks
• Intrinsic degree-correlations in static model of scale-free networks
• Diffusion in scale-free networks with annealed disorder
• Multicomponent reaction-diffusion processes on complex networks
• Organization of complex networks without multiple connections

Cited by in corpus (20)

• Epidemic processes in complex networks
• Competing activation mechanisms in epidemics on networks
• Langevin approach for the dynamics of the contact process on annealed scale-free networks
• Mean-field diffusive dynamics on weighted networks
• Portraits of Complex Networks
• Zero Pearson Coefficient for Strongly Correlated Growing Trees
• Spectral properties and the accuracy of mean-field approaches for epidemics on correlated networks
• Controlling epidemics through optimal allocation of test kits and vaccine doses across networks
• Measuring degree-degree association in networks
• Generating random networks with given degree-degree correlations and degree-dependent clustering
• High prevalence regimes in the pair quenched mean-field theory for the susceptible-infected-susceptible model on networks
• Dynamics to equilibrium in Network Games: individual behavior and global response
• Critical Boolean networks with scale-free in-degree distribution
• Observability transitions in correlated networks
• Link-based formalism for time evolution of adaptive networks
• Designing Networks: A Mixed-Integer Linear Optimization Approach
• Influence of individual nodes for continuous-time Susceptible-Infected-Susceptible dynamics on synthetic and real-world networks
• Diffusion on assortative networks: from mean-field to agent-based, via Newman rewiring
• Reconstruction of evolved dynamic networks from degree correlations
• Diagonal degree correlations vs. epidemic threshold in scale-free networks