2009/11/30 by S. S. Manna, Arnab Chatterjee · 81 citations
Mathematics · Physics and Astronomy · #Cluster (spacecraft) #Combinatorics #Complex Network Analysis Techniques #Complex network #Computer science #Distribution (mathematics) #Explosive material #Geography #Graph #Lattice (music) #Mathematical analysis #Mathematics #Order (exchange) #Percolation (cognitive psychology) #Physics #Power law #Preferential attachment #Random graph #Square lattice #Stable distribution #Statistical physics #Statistics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech #physics.comp-ph
paper · pdf · doi:10.1016/j.physa.2010.10.009
published in Physica A Statistical Mechanics and its Applications 390(2), 177-182 (Elsevier BV) · 4 pages, 5 figures
arxiv created 2010/10/07 · openalex publication_date 2010/10/15 · arxiv updated 2011/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The biased link occupation rule in the Achlioptas process (AP) discourages the large clusters to grow much ahead of others and encourages faster growth of clusters which lag behind. In this paper we propose a model where this tendency is sharply reflected in the Gamma distribution of the cluster sizes, unlike the power law distribution in AP. In this model single edges between pairs of clusters of sizes si and sj are occupied with a probability ∝ (sisj)α. The parameter α is continuously tunable over the entire real axis. Numerical studies indicate that for α< αc the transition is first order, αc=0 for square lattice and αc=-1/2 for random graphs. In the limits of α= -∞, +∞ this model coincides with models well established in the literature.