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Triadic Closure in Configuration Models with Unbounded Degree Fluctuations.
- Source :
-
Journal of Statistical Physics . Nov2018, Vol. 173 Issue 3/4, p746-774. 29p. - Publication Year :
- 2018
-
Abstract
- The configuration model generates random graphs with any given degree distribution, and thus serves as a null model for scale-free networks with power-law degrees and unbounded degree fluctuations. For this setting, we study the local clustering c(k), i.e., the probability that two neighbors of a degree-k node are neighbors themselves. We show that c(k) progressively falls off with k and the graph size n and eventually for k=Ω(n) settles on a power law c(k)∼n5-2τk-2(3-τ) with τ∈(2,3) the power-law exponent of the degree distribution. This fall-off has been observed in the majority of real-world networks and signals the presence of modular or hierarchical structure. Our results agree with recent results for the hidden-variable model and also give the expected number of triangles in the configuration model when counting triangles only once despite the presence of multi-edges. We show that only triangles consisting of triplets with uniquely specified degrees contribute to the triangle counting. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00224715
- Volume :
- 173
- Issue :
- 3/4
- Database :
- Academic Search Index
- Journal :
- Journal of Statistical Physics
- Publication Type :
- Academic Journal
- Accession number :
- 133019460
- Full Text :
- https://doi.org/10.1007/s10955-018-1952-x