Tuning clustering in random networks with arbitrary degree distributions

Abstract

We present a generator of random networks where both the degree-dependent clustering coefficient and the degree distribution are tunable. Following the same philosophy as in the configuration model, the degree distribution and the clustering coefficient for each class of nodes of degree $k$ are fixed ad hoc and a priori. The algorithm generates corresponding topologies by applying first a closure of triangles and secondly the classical closure of remaining free stubs. The procedure unveils an universal relation among clustering and degree-degree correlations for all networks, where the level of assortativity establishes an upper limit to the level of clustering. Maximum assortativity ensures no restriction on the decay of the clustering coefficient whereas disassortativity sets a stronger constraint on its behavior. Correlation measures in real networks are seen to observe this structural bound.

References in corpus (26)

• Statistical mechanics of complex networks
• The structure and function of complex networks
• Uncovering the overlapping community structure of complex networks in nature and society
• Lethality and centrality in protein networks
• Random graphs with arbitrary degree distributions and their applications
• Evolution of networks
• Who is the best connected scientist? A study of scientific coauthorship networks
• Defining and identifying communities in networks
• Hierarchical Organization in Complex Networks
• Self-similar community structure in organisations
• Dynamical and correlation properties of the Internet
• Growing Scale-Free Networks with Tunable Clustering
• Generation of uncorrelated random scale-free networks
• Large-scale topological and dynamical properties of Internet
• Topology of the World Trade Web
• Epidemic spreading in correlated complex networks
• Absence of epidemic threshold in scale-free networks with connectivity correlations
• Class of correlated random networks with hidden variables
• The topological relationship between the large-scale attributes and local interaction patterns of complex networks
• Cut-offs and finite size effects in scale-free networks
• Generic scale of the "scale-free" growing networks
• The origin of degree correlations in the Internet and other networks
• Rate equation approach for correlations in growing network models
• Random Networks with Tunable Degree Distribution and Clustering
• Uncorrelated Random Networks
• Perturbing General Uncorrelated Networks

Cited by in corpus (56)

• Epidemic processes in complex networks
• Networks beyond pairwise interactions: structure and dynamics
• Hyperbolic Geometry of Complex Networks
• The Kuramoto model in complex networks
• Popularity versus Similarity in Growing Networks
• Random graphs with clustering
• Percolation on complex networks: Theory and application
• Bipartite Graphs as Models of Complex Networks
• Percolation and Epidemic Thresholds in Clustered Networks
• Quantifying randomness in real networks
• Analysis of complex contagions in random multiplex networks
• Clustering in complex networks. I. General formalism
• Systematic Topology Analysis and Generation Using Degree Correlations
• Clustering in complex networks. II. Percolation properties
• Networks of strong ties
• Bond percolation on a class of clustered random networks
• Evolving Clustered Random Networks
• Multifractal Network Generator
• Robustness of partially interdependent network formed of clustered networks
• Clustering Drives Assortativity and Community Structure in Ensembles of Networks
• Social cohesion, structural holes, and a tale of two measures
• Constrained Markovian dynamics of random graphs
• Spectra of networks containing short loops
• Generation of arbitrarily two-point correlated random networks
• Tailored graph ensembles as proxies or null models for real networks I: tools for quantifying structure
• Clustering Phase Transitions and Hysteresis: Pitfalls in Constructing Network Ensembles
• Randomizing hypergraphs preserving degree correlation and local clustering
• Ising model in clustered scale-free networks
• Generating random networks with given degree-degree correlations and degree-dependent clustering
• Clustering in random line graphs
• Assortative Mixing in Close-Packed Spatial Networks
• Coupled dynamics of node and link states in complex networks: A model for language competition
• Networks with arbitrary edge multiplicities
• A general formulation of long-range degree correlations in complex networks
• Tuning the average path length of complex networks and its influence to the emergent dynamics of the majority-rule model
• Motifs in Triadic Random Graphs based on Steiner Triple Systems
• Effect of network clustering on mutually cooperative coinfections
• Self-avoiding walks and connective constants in clustered scale-free networks
• Tuning degree distributions of scale-free networks
• On the effect of the path length and transitivity of small-world networks on epidemic dynamics
• Tuning the Clustering Coefficient of Generalized Circulant Networks
• Degree correlations in graphs with clique clustering
• Structure constrained by metadata in networks of chess players
• Generalized preferential attachment: tunable power-law degree distribution and clustering coefficient
• Exponential rate of epidemic spreading on complex networks
• Coarse-graining the dynamics of network evolution: the rise and fall of a networked society
• Emergence of Long-Range Correlations in Random Networks
• Designing Networks: A Mixed-Integer Linear Optimization Approach
• Synergistic epidemic spreading in correlated networks
• The scaling of human interactions with city size
• Observability transitions in clustered networks
• Generating Scale-free Networks with Adjustable Clustering Coefficient Via Random Walks
• Reconstruction of evolved dynamic networks from degree correlations
• 2.5K-Graphs: from Sampling to Generation
• On the Role of Triadic Substructures in Complex Networks
• On the Controllability of Clustered Scale-Free Networks