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

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  • Massen, Claire P.
  • Doye, Jonathan P.K.

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 (IS) 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 potential 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.

Suggested Citation

  • Massen, Claire P. & Doye, Jonathan P.K., 2007. "A self-consistent approach to measure preferential attachment in networks and its application to an inherent structure network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 377(1), pages 351-362.
    • Handle: RePEc:eee:phsmap:v:377:y:2007:i:1:p:351-362
    DOI: 10.1016/j.physa.2006.11.007
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    References listed on IDEAS

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    1. Dorogovtsev, S.N. & Mendes, J.F.F., 2003. "Evolution of Networks: From Biological Nets to the Internet and WWW," OUP Catalogue, Oxford University Press, number 9780198515906.
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    1. Tomassini, Marco & Luthi, Leslie, 2007. "Empirical analysis of the evolution of a scientific collaboration network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(2), pages 750-764.
    2. Sheridan, Paul & Yagahara, Yuichi & Shimodaira, Hidetoshi, 2012. "Measuring preferential attachment in growing networks with missing-timelines using Markov chain Monte Carlo," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(20), pages 5031-5040.

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