Random graphs with clustering.

By Mark Newman. Physical Review Letters, 2009

454 citations recorded by the source corpus.

We offer a solution to a long-standing problem in the theory of networks, the creation of a plausible, solvable model of a network that displays clustering or transitivity--the propensity for two neighbors of a network node also to be neighbors of one another. We show how standard random-graph models can be generalized to incorporate clustering and give exact solutions for various properties of the resulting networks, including sizes of network components, size of the giant component if there is one, position of the phase transition at which the giant component forms, and position of the phase transition for percolation on the network.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/dbc990ba91d52d409a9f6abd2a964ed4c5ade697

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In Computational Theory and Mathematics

In Geometry and Topology

In Statistical and Nonlinear Physics

Citations in the corpus

Robustness and resilience of complex networks (2024, unknown): “Depending on how clustering is defined and on whether its value is high or low, the network might be considered more or less robust than its unclustered counterpart 105–108 .”
Multilayer networks (2013, methodology): “[167, 297] studied percolation cascades in interdependent networks in which intra-layer networks are produced using monoplex random-graph models with clustering (in particular, by using the degree-triangle model [244]).”
Suppressing cascades of load in interdependent networks (2011, background): “[66] Newman MEJ (2009) Random graphs with clustering.”
The Kuramoto model in complex networks (2015, methodology): “Nevertheless, even though T achieved for high 〈k〉 is not as high as the ones achieved by stochastic rewiring algorithms [103, 113–116], it is possible to obtain a significantly higher clustering than those obtained in random network models [109, 110].”
Random Graphs and Complex Networks (2016, background): “In [201], Newman performs a generating function analysis of when a giant component is expected to exist.”
Networks and the Epidemiology of Infectious Disease (2010, background): “The calculation of the invasion threshold for the recently defined triangular configuration model [118, 119] involves calculating both the expected number of secondary infectious individuals and triangles rather than just working at the individual level.”
Binary-state dynamics on complex networks: pair approximation and beyond (2012, unknown): “[50–53].”
The statistical physics of real-world networks (2018, background): “g(z) = ∑ k z P (k) for the degree distribution [157, 167], yet is rigorously defined only for infinite and locally tree-like networks—even if it often works surprisingly well for real networks [168].”