title: Revising the simple measures of assortativity in complex networks.
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.
authors.affiliation: School of Communication and Electronics Engineering, Qingdao Technological University, Qingdao 266520, China. xiaokeeie@gmail.com
authors.forename: Xiao-Ke
authors.initials: XK
authors.lastname: Xu
authors.forename: Jie
authors.initials: J
authors.lastname: Zhang
authors.forename: Junfeng
authors.initials: J
authors.lastname: Sun
authors.forename: Michael
authors.initials: M
authors.lastname: Small
mesh_terms: D000465:Algorithms; D001703:Biophysics / Q000379:methods*; D015233:Models, Statistical; D009415:Nerve Net; D016571:Neural Networks, Computer; D011506:Proteins / Q000737:chemistry; D015203:Reproducibility of Results
chemical_list: D011506:Proteins