Growing scale-free networks with tunable clustering.

By Petter Holme, Beom Jun Kim. Physical review. E, Statistical, nonlinear, and soft matter physics, 2001

1,060 citations recorded by the source corpus.

We extend the standard scale-free network model to include a "triad formation step." We analyze the geometric properties of networks generated by this algorithm both analytically and by numerical calculations, and find that our model possesses the same characteristics as the standard scale-free networks such as the power-law degree distribution and the small average geodesic length, but with the high clustering at the same time. In our model, the clustering coefficient is also shown to be tunable simply by changing a control parameter---the average number of triad formation trials per time step.

Subfields: Condensed Matter Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/b3c081e9c6f21ec9867d70b8a382c44f6e760276

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In Condensed Matter Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Design Space for Graph Neural Networks (2020, methodology): “We use two families of graphs prevalent in the real-world small-world [33] and scale-free graphs [9], which have diverse structural properties, measured by a suite of graph statistics .”
Attack Robustness and Centrality of Complex Networks (2013, methodology): “Figure 4 shows robustness results for scale-free networks with different clustering coefficients (generated using the Holme-Kim model [31]).”
Resisting structural re-identification in anonymized social networks (2008, methodology): “We also include a synthetic graph, Clustered PowerLaw, which is similar to Power-Law except that the random graph generation process is biased to introduce triangles [22].”
Analyzing and modeling real-world phenomena with complex networks: a survey of applications (2007, methodology): “Rosato and Tiriticco simulated the growth of the Internet at AS level [213] using a mechanism of triad formation introduced in [214].”
Bipartite Graphs as Models of Complex Networks (2003, methodology): “In [59], for each newly created edge, a triangle is built using both extremities of this edge and a neighbor of the old vertex.”
Growth of the flickr social network (2008, background): “to add a tunable level of clustering [7].”
Limited individual attention and online virality of low-quality information (2017, result): “The results generalize to larger and sparser networks with higher clustering coefficient [31].”
The Structure and Function of Complex Networks (2003, background): “For example, a number of authors [30, 102, 198, 217, 220, 242, 397, 398, 411, 412] have studied models of network transitivity that make use of “triadic closure” processes.”
Identity-aware Graph Neural Networks (2021, methodology): “In Table 2, we observe that adding identity information results in a 55% and 42.3% increase in best performance over ScaleFree and SmallWorld graphs respectively.”
Structure and time evolution of an Internet dating community (2002, background): “In an Internet community the way by which people introduce strangers among their acquaintances to each other (Newman 2001; Holme and Kim 2002) is likely not the mechanism responsible for the finite clustering (remember that in network models such as the Erdös-Rényi (1959) and Barabási-Albert (Barabá”