Random Networks with Tunable Degree Distribution and Clustering

Abstract

We present an algorithm for generating random networks with arbitrary degree distribution and Clustering (frequency of triadic closure). We use this algorithm to generate networks with exponential, power law, and poisson degree distributions with variable levels of clustering. Such networks may be used as models of social networks and as a testable null hypothesis about network structure. Finally, we explore the effects of clustering on the point of the phase transition where a giant component forms in a random network, and on the size of the giant component. Some analysis of these effects is presented.

9 pages, 13 figures corrected typos, added two references, reorganized references

References in corpus (19)

• Statistical mechanics of complex networks
• The structure and function of complex networks
• Error and attack tolerance of complex networks
• Hierarchical organization of modularity in metabolic networks
• Random graphs with arbitrary degree distributions and their applications
• Evolution of networks
• Mixing patterns in networks
• Classes of behavior of small-world networks
• Hierarchical Organization in Complex Networks
• Breakdown of the Internet under intentional attack
• Structure of Growing Networks: Exact Solution of the Barabasi--Albert's Model
• Growing Scale-Free Networks with Tunable Clustering
• Organization of Growing Random Networks
• Dynamics of rumor propagation on small-world networks
• Properties of highly clustered networks
• Emergence of a small world from local interactions: Modeling acquaintance networks
• On the uniform generation of random graphs with prescribed degree sequences
• Performance of networks of artificial neurons: The role of clustering
• How to generate a random growing network

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• Bond percolation on a class of clustered random networks
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• A Dynamic Model of Cascades on Random Networks with a Threshold Rule
• Clustering Phase Transitions and Hysteresis: Pitfalls in Constructing Network Ensembles
• Epidemic spreading on preferred degree adaptive networks
• Endemic infections are always possible on regular networks
• Tuning the average path length of complex networks and its influence to the emergent dynamics of the majority-rule model
• Complex networks as an emerging property of hierarchical preferential attachment
• Tuning degree distributions of scale-free networks
• On the effect of the path length and transitivity of small-world networks on epidemic dynamics
• Compact pairwise models for epidemics with multiple infectious stages on degree heterogeneous and clustered networks
• Generalized preferential attachment: tunable power-law degree distribution and clustering coefficient
• Coarse-graining the dynamics of network evolution: the rise and fall of a networked society
• SIR epidemics in dynamic contact networks
• Designing Networks: A Mixed-Integer Linear Optimization Approach
• Observability transitions in clustered networks
• Exact deterministic representation of Markovian SIR epidemics on networks with and without loops
• Relaxation dynamics of maximally clustered networks
• Tomography of random social networks
• Arbitrary degree distribution and high clustering in networks of locally interacting agents