Universal properties of growing networks

2004/06/02 by P. L. Krapivsky, Bernard Derrida, B. Derrida
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Opinion Dynamics and Social Influence #Stochastic processes and statistical mechanics #cond-mat.dis-nn

paper · pdf · doi:10.1016/j.physa.2004.05.020

published as Physica A 340 (2004) 714--724 · 14 pages, 1 figure

openalex publication_date 2004/06/02 · arxiv created 2004/08/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Networks growing according to the rule that every new node has a probability p_k of being attached to k preexisting nodes, have a universal phase diagram and exhibit power law decays of the distribution of cluster sizes in the non-percolating phase. The percolation transition is continuous but of infinite order and the size of the giant component is infinitely differentiable at the transition (though of course non-analytic). At the transition the average cluster size (of the finite components) is discontinuous.

Citations

• Anomalous percolation properties of growing networks
• Singularity Analysis of Generating Functions
• Ordering, metastability and phase transitions in two-dimensional systems
• Statistical mechanics of complex networks