The mathematics of non-linear metrics for nested networks
The mathematics of non-linear metrics for nested networks
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嵌套网络非线性度量的数学
DOI：
10.1016/j.physa.2016.05.023
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发表时间：
2016-10-15
影响因子：
3.3
通讯作者：
Mariani, Manuel Sebastian
中科院分区：
文献类型：
--
作者：
Wu, Rui-Jie;Shi, Gui-Yuan;Mariani, Manuel Sebastian
国际贸易和生态网络的数据的数值分析表明，非线性适应度复杂性度量是最好的候选人排名节点的重要性在二分网络，表现出嵌套结构。尽管它与真实的网络相关，但该度量及其变体的数学性质在很大程度上仍未被探索。在这里，我们进行分析和数值研究的健身复杂性度量和一个新的变种，称为最小极值度量。我们严格推导出精确的表达式，完美的嵌套网络的节点得分，并表明这些表达式解释了非平凡的收敛性能的度量。在真实的数据上的适应度复杂性度量和最小极值度量之间的比较表明，如果输入数据是可靠的，后者可以产生改进的排名。(C)2016爱思唯尔B.V.保留所有权利。
Numerical analysis of data from international trade and ecological networks has shown that the non-linear fitness complexity metric is the best candidate to rank nodes by importance in bipartite networks that exhibit a nested structure. Despite its relevance for real networks, the mathematical properties of the metric and its variants remain largely unexplored. Here, we perform an analytic and numeric study of the fitness complexity metric and a new variant, called minimal extremal metric. We rigorously derive exact expressions for node scores for perfectly nested networks and show that these expressions explain the non-trivial convergence properties of the metrics. A comparison between the fitness complexity metric and the minimal extremal metric on real data reveals that the latter can produce improved rankings if the input data are reliable. (C) 2016 Elsevier B.V. All rights reserved.