Abstract
In this paper, we present trapping issues of weight-dependent walks on weighted hierarchical networks which are based on the classic scale-free hierarchical networks. Assuming that edge’s weight is used as local information by a random walker, we introduce a biased walk. The biased walk is that a walker, at each step, chooses one of its neighbours with a probability proportional to the weight of the edge. We focus on a particular case with the immobile trap positioned at the hub node which has the largest degree in the weighted hierarchical networks. Using a method based on generating functions, we determine explicitly the mean first-passage time (MFPT) for the trapping issue. Let parameter a (0 < a < 1) be the weight factor. We show that the efficiency of the trapping process depends on the parameter a; the smaller the value of a, the more efficient is the trapping process.
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Acknowledgements
This research is supported by the National Science Foundation of China (11071224) and the Priority Academic Program Development of Jiangsu Higher Education Institutions.
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DAI, M., LIU, J. & ZHU, F. Biased trapping issue on weighted hierarchical networks. Pramana - J Phys 83, 481–491 (2014). https://doi.org/10.1007/s12043-014-0814-6
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DOI: https://doi.org/10.1007/s12043-014-0814-6