The largest component in a subcritical random graph with a power law degree distribution

By Svante Janson. 2007

51 citations recorded by the source corpus.

It is shown that in a subcritical random graph with given vertex degrees satifying a power law degree distribution with exponent > 3, the largest component is of order n 1/( 1) . More precisely, the order of the largest component is approximatively given by a simple constant times the largest vertex degree. These results are extended to several other random graph models with power law degree distributions. This proves a conjecture by Durrett.

Subfields: Discrete Mathematics and Combinatorics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/d525a56e2ac5b18b1c238ab46b6e45dc302fa58b

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In Discrete Mathematics and Combinatorics

In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

The component sizes of a critical random graph with given degree sequence (2010, background): “Requiring a fourth moment condition, Janson and Luczak [18] proved that if n1/3αn → ∞, then the size of the largest component of G(n,d(n)) divided by nαn converges in probability to 2μ β , while the size of the second largest component of G(n,d(n)) divided by nαn converges in probability to 0, where”
Random Graphs and Complex Networks (2016, background): “19 is proved by Janson (2008). (Janson, 2008, Theorem 1.”
Critical phenomena in complex networks (2007, background): “In uncorrelated scale-free networks without a giant connected component, the largest connected component contains ∼ N vertices (Durrett, 2006; Janson, 2007), where we assume γ > 3.”
Novel scaling limits for critical inhomogeneous random graphs (2009, unknown): “, the results by Janson in [24] or Theorem 1.”