2009/07/31 by Y. S. Cho, J. S. Kim, Jae Il Park +4 · 175 citations
Mathematics · Physics and Astronomy · #Biology #Combinatorics #Complex Network Analysis Techniques #Complex network #Condensed matter physics #Degree (music) #Degree distribution #Electrical resistivity and conductivity #Exponent #Mathematics #Opinion Dynamics and Social Influence #Percolation (cognitive psychology) #Percolation threshold #Physics #Quantum mechanics #Scale (ratio) #Scale-free network #Statistical physics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevlett.103.135702
published in Physical Review Letters 103(13), 135702 (American Physical Society) · 4 pages, 6 figures
openalex publication_date 2009/09/23 · arxiv created 2009/09/24 · arxiv updated 2015/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
It has been recently shown that the percolation transition is discontinuous in Erdos-Rényi networks and square lattices in two dimensions under the Achlioptas process (AP). Here, we show that when the structure is highly heterogeneous as in scale-free networks, a discontinuous transition does not always occur: a continuous transition is also possible depending on the degree distribution of the scale-free network. This originates from the competition between the AP that discourages the formation of a giant component and the existence of hubs that encourages it. We also estimate the value of the characteristic degree exponent that separates the two transition types.