Counting triangles in power-law uniform random graphs

5Citations
Citations of this article
8Readers
Mendeley users who have this article in their library.

Abstract

We count the asymptotic number of triangles in uniform random graphs where the degree distribution follows a power law with degree exponent τ∈(2,3). We also analyze the local clustering coefficient c(k), the probability that two random neighbors of a vertex of degree k are connected. We find that the number of triangles, as well as the local clustering coefficient, scale similarly as in the erased configuration model, where all self-loops and multiple edges of the configuration model are removed. Interestingly, uniform random graphs contain more triangles than erased configuration models with the same degree sequence. The number of triangles in uniform random graphs is closely related to that in a version of the rank-1 inhomogeneous random graph, where all vertices are equipped with weights, and the probabilities that edges are present are moderated by asymptotically linear functions of the products of these vertex weights.

References Powered by Scopus

A critical point for random graphs with a given degree sequence

1745Citations
N/AReaders
Get full text

A Probabilistic Proof of an Asymptotic Formula for the Number of Labelled Regular Graphs

761Citations
N/AReaders
Get full text

Large-scale topological and dynamical properties of the Internet

598Citations
N/AReaders
Get full text

Cited by Powered by Scopus

Optimal subgraph structures in scale-free configuration models

8Citations
N/AReaders
Get full text

Extreme Value Statistics for Evolving Random Networks

2Citations
N/AReaders
Get full text

Distinguishing Power-Law Uniform Random Graphs from Inhomogeneous Random Graphs Through Small Subgraphs

2Citations
N/AReaders
Get full text

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Cite

CITATION STYLE

APA

Gao, P., van der Hofstad, R., Southwell, A., & Stegehuis, C. (2020). Counting triangles in power-law uniform random graphs. Electronic Journal of Combinatorics, 27(3), 1–28. https://doi.org/10.37236/9239

Readers over time

‘18‘20‘21‘23‘2400.511.52

Readers' Seniority

Tooltip

PhD / Post grad / Masters / Doc 4

67%

Lecturer / Post doc 1

17%

Researcher 1

17%

Readers' Discipline

Tooltip

Computer Science 3

60%

Mathematics 1

20%

Arts and Humanities 1

20%

Save time finding and organizing research with Mendeley

Sign up for free
0