2007/06/30 by M. E. J. Newman · 1 citation
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Opinion Dynamics and Social Influence #Stochastic processes and statistical mechanics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.76.045101
published as Phys. Rev. E 76, 045101 (2007) · 5 pages, 1 figure
arxiv created 2007/06/30 · openalex publication_date 2007/10/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give an exact solution for the complete distribution of component sizes in random networks with arbitrary degree distributions. The solution tells us the probability that a randomly chosen node belongs to a component of size s for any s . We apply our results to networks with the three most commonly studied degree distributions-Poisson, exponential, and power-law-as well as to the calculation of cluster sizes for bond percolation on networks, which correspond to the sizes of outbreaks of epidemic processes on the same networks. For the particular case of the power-law degree distribution, we show that the component size distribution itself follows a power law everywhere below the phase transition at which a giant component forms, but takes an exponential form when a giant component is present.