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A self-consistent approach to measure preferential attachment in networks and its application to an inherent structure networkClaire P. Massen and Jonathan P. K. DoyePhysica A 377, 351-362 (2007)AbstractPreferential 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. Any such method will have associated uncertainties because the network growth is stochastic. 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. Hence, we show that a preferential attachment rule does apply to the inherent structure network. However, the scale-free degree distribution is different to that of a model network grown using the obtained preferential attachment rules, implying that other factors are also important in the growth process.The full paper is available from Physica A and arXiv.org. |