2017/12/14 by Haggai Bonneau, A. Hassid, Aviv Hassid +4 · 26 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Average path length #Bioinformatics and Genomic Networks #Combinatorics #Complex Network Analysis Techniques #Complex network #Computer science #Degree distribution #Distribution (mathematics) #Fraction (chemistry) #Graph #Mathematical analysis #Mathematics #Path length #Physics #Poisson distribution #Random graph #Shortest path problem #Statistical physics #Statistics #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech #physics.soc-ph
paper · pdf · doi:10.1103/physreve.96.062307
published in Physical review. E 96(6), 062307 (American Physical Society) · 44 pages, 11 figures
openalex publication_date 2017/12/14 · arxiv created 2017/12/15 · arxiv updated 2017/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present analytical results for the distribution of shortest cycle lengths (DSCL) in random networks. The approach is based on the relation between the DSCL and the distribution of shortest path lengths (DSPL). We apply this approach to configuration model networks, for which analytical results for the DSPL were obtained before. We first calculate the fraction of nodes in the network which reside on at least one cycle. Conditioning on being on a cycle, we provide the DSCL over ensembles of configuration model networks with degree distributions which follow a Poisson distribution (Erdős-Rényi network), degenerate distribution (random regular graph), and a power-law distribution (scale-free network). The mean and variance of the DSCL are calculated. The analytical results are found to be in very good agreement with the results of computer simulations.