经济和金融网络中的风险依赖中心性
Risk-dependent centrality in economic and financial networks
摘要：
节点中心性是复杂网络研究中最重要、应用最广泛的概念之一。在这里，我们扩展了金融和经济网络中的节点中心性的范式，以考虑节点“重要性”的变化，不仅由系统的拓扑结构的变化，而且作为网络作为一个整体提交的外部风险水平的结果。从"易感-感染"（SI）流行病模型及其与网络可通信性函数的关系出发，我们为（金融和经济）网络中的节点开发了一系列风险依赖的中心性。我们在这里分析这些风险依赖的中心性措施的一些最重要的数学性质。特别是，我们研究了新观察到的排名交错现象，通过这种现象，两个实体可能会在网络中的风险方面交错其排名位置，这仅仅是外部条件变化的结果，即，而不改变拓扑结构。我们通过研究两个真实世界的系统来测试风险依赖的中心性：标准普尔100指数的资产收集网络和美国顶级公司的公司董事会网络，根据福布斯1999年的报道。我们发现，根据其风险依赖的中心性，在所分析的金融公司的排名中的高位置对应于在危机期间对外部市场变化更敏感的公司。
英文摘要：
Node centrality is one of the most important and widely used concepts in the study of complex networks. Here, we extend the paradigm of node centrality in financial and economic networks to consider the changes of node "importance" produced not only by the variation of the topology of the system but also as a consequence of the external levels of risk to which the network as a whole is submitted. Starting from the "Susceptible-Infected" (SI) model of epidemics and its relation to the communicability functions of networks we develop a series of risk-dependent centralities for nodes in (financial and economic) networks. We analyze here some of the most important mathematical properties of these risk-dependent centrality measures. In particular, we study the newly observed phenomenon of ranking interlacement, by means of which two entities may interlace their ranking positions in terms of risk in the network as a consequence of the change in the external conditions only, i.e., without any change in the topology. We test the risk-dependent centralities by studying two real-world systems: the network generated by collecting assets of the S\&P 100 and the corporate board network of the US top companies, according to Forbes in 1999. We found that a high position in the ranking of the analyzed financial companies according to their risk-dependent centrality corresponds to companies more sensitive to the external market variations during the periods of crisis.
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