SIAM Journal on Financial Mathematics, Volume 11, Issue 2, Page 526-565, January 2020.
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 subjected. 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 U.S. 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.

中文翻译：

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经济和金融网络中风险相关的中心性

SIAM金融数学杂志，第11卷，第2期，第526-565页，2020年1月。
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节点中心性的范式，以考虑节点“重要性”的变化，这不仅是由于系统拓扑结构的变化而产生的，而且是由于网络外部风险水平而产生的整体而言。从“流行病的易感性”（SI）模型及其与网络的通信功能的关系开始，我们为（金融和经济）网络中的节点开发了一系列风险相关的中心。我们在这里分析这些风险相关的集中度度量的一些最重要的数学属性。特别是，我们研究了新发现的隔行排序现象，通过这种方式，两个实体可以仅由于外部条件的变化（即，拓扑没有任何变化）就网络中的风险而言交错其排名位置。根据1999年《福布斯》的报道，我们通过研究两个现实世界的系统来测试与风险相关的中心性：通过收集标准普尔100指数资产产生的网络以及美国顶尖公司的公司董事会网络。根据风险相关的中心度对被分析的金融公司进行排名，对应于在危机期间对外部市场变化更为敏感的公司。