Percolation on shopping and cashback electronic commerce networks

Tao Fu, Yini Chen, Zhen Qin and Liping Guo

Physica A: Statistical Mechanics and its Applications, 2013, vol. 392, issue 12, 2807-2820

Abstract: Many realistic networks live in the form of multiple networks, including interacting networks and interdependent networks. Here we study percolation properties of a special kind of interacting networks, namely Shopping and Cashback Electronic Commerce Networks (SCECNs). We investigate two actual SCECNs to extract their structural properties, and develop a mathematical framework based on generating functions for analyzing directed interacting networks. Then we derive the necessary and sufficient condition for the absence of the system-wide giant in- and out- component, and propose arithmetic to calculate the corresponding structural measures in the sub-critical and supercritical regimes. We apply our mathematical framework and arithmetic to those two actual SCECNs to observe its accuracy, and give some explanations on the discrepancies. We show those structural measures based on our mathematical framework and arithmetic are useful to appraise the status of SCECNs. We also find that the supercritical regime of the whole network is maintained mainly by hyperlinks between different kinds of websites, while those hyperlinks between the same kinds of websites can only enlarge the sizes of in-components and out-components.

Keywords: Interacting networks; Percolation; Generating function; Directed graph (search for similar items in EconPapers)
Date: 2013
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:392:y:2013:i:12:p:2807-2820

DOI: 10.1016/j.physa.2013.02.018

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