A self-consistent approach to measure preferential attachment in networks and its application to an inherent structure network

2005/12/31 by Claire P. Massen, Jonathan P. K. Doye
Chemistry · Mathematics · Physics and Astronomy · #Biological system #Biology #Chemical physics #Chemistry #Complex Network Analysis Techniques #Complex network #Computer science #Data mining #Energy (signal processing) #Energy landscape #Function (biology) #Mathematics #Maxima and minima #Measure (data warehouse) #Network formation #Network model #Opinion Dynamics and Social Influence #Physics #Preferential attachment #Process (computing) #Scale (ratio) #Scale-free network #Statistical physics #Statistics #Theoretical and Computational Physics #Thermodynamics #cond-mat.stat-mech

paper · pdf · doi:10.1016/j.physa.2006.11.007

published as Physica A, 377, 351-362 (2007) · 8 pages, 8 figures

arxiv created 2006/04/25 · openalex publication_date 2006/11/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Preferential attachment is one possible way to obtain a scale-free network. We develop a self-consistent method to determine whether preferential attachment occurs during the growth of a network, and to extract the preferential attachment rule using time-dependent data. Model networks are grown with known preferential attachment rules to test the method, which is seen to be robust. The method is then applied to a scale-free inherent structure network, which represents the connections between minima via transition states on a potential energy landscape. Even though this network is static, we can examine the growth of the network as a function of a threshold energy (rather than time), where only those transition states with energies lower than the threshold energy contribute to the network.For these networks we are able to detect the presence of preferential attachment, and this helps to explain the ubiquity of funnels on energy landscapes. However, the scale-free degree distribution shows some differences from that of a model network grown using the obtained preferential attachment rules, implying that other factors are also important in the growth process.

Citations

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