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Revising the simple measures of assortativity in complex networks
Xiao-Ke Xu1, Jie Zhang, Junfeng Sun
1School of Communication and Electronics Engineering, Qingdao Technological University, Qingdao 266520, China. xiaokeeie@gmail.com
Abstract:
We find that traditional statistics for measuring degree mixing are strongly affected by superrich nodes. To counteract and measure the effect of superrich nodes, we propose a paradigm to quantify the mixing pattern of a real network in which different mixing patterns may appear among low-degree nodes and among high-degree nodes. This paradigm and the simple revised measure uncover the true complex degree mixing patterns of complex networks with superrich nodes. The alternate method indicates that some networks show a false disassortative mixing induced by superrich nodes and have no tendency to be genuinely disassortative. Our results also show that the previously observed fragility of scale-free networks is actually greatly exacerbated by the presence of even a very small number of superrich nodes.
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