标题： 非线性度量在嵌套网络中的数学方法 显示英文标题

标题： The mathematics of non-linear metrics for nested networks

摘要： 对国际贸易和生态网络数据的数值分析表明，非线性适应度-复杂度度量是排名具有嵌套结构的双部网络中节点重要性的最佳候选指标。 尽管该度量及其变体在真实网络中具有相关性，但其数学性质仍大多未被探索。 在此，我们对适应度-复杂度度量和一种新的变体——最小极值度量进行了分析和数值研究。 我们严格推导了完美嵌套网络中节点得分的精确表达式，并表明这些表达式解释了度量的非平凡收敛特性。 在真实数据上对适应度-复杂度度量和最小极值度量进行比较显示，如果输入数据可靠，后者可以产生改进的排名。 显示英文摘要

摘要： 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.