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A Community-Structure-Based Method for Estimating the Fractal Dimension, and its Application to Water Networks for the Assessment of Vulnerability to Disasters
Water Resources Management ( IF 4.3 ) Pub Date : 2021-03-13 , DOI: 10.1007/s11269-021-02773-y
C. Giudicianni , A. Di Nardo , R. Greco , A. Scala

Most real-world networks, from the World-Wide-Web to biological systems, are known to have common structural properties. A remarkable point is fractality, which suggests the self-similarity across scales of the network structure of these complex systems. Managing the computational complexity for detecting the self-similarity of big-sized systems represents a crucial problem. In this paper, a novel algorithm for revealing the fractality, that exploits the community structure principle, is proposed and then applied to several water distribution systems (WDSs) of different size, unveiling a self-similar feature of their layouts. A scaling-law relationship, linking the number of clusters necessary for covering the network and their average size is defined, the exponent of which represents the fractal dimension. The self-similarity is then investigated as a proxy of recurrent and specific response to multiple random pipe failures – like during natural disasters – pointing out a specific global vulnerability for each WDS. A novel vulnerability index, called Cut-Vulnerability is introduced as the ratio between the fractal dimension and the average node degree, and its relationships with the number of randomly removed pipes necessary to disconnect the network and with some topological metrics are investigated. The analysis shows the effectiveness of the novel index in describing the global vulnerability of WDSs.



中文翻译:

基于社区结构的分形维数估计方法及其在水网络中评估灾害脆弱性的应用

从万维网到生物系统,大多数现实世界的网络都具有共同的结构特性。一个值得注意的点是分形性,它表明了这些复杂系统的网络结构在各个尺度上的自相似性。管理用于检测大型系统的自相似性的计算复杂性是一个关键问题。本文提出了一种利用社区结构原理揭示分形的新算法,并将其应用于几种不同大小的供水系统,揭示了其布局的自相似特征。定义了比例定律关系,将覆盖网络所需的簇数及其平均大小联系起来,其指数表示分形维数。然后研究自相似性,以作为对多个随机管道故障(例如自然灾害期间)的周期性和特定响应的代理,指出每个WDS的特定全局漏洞。一种新的漏洞指数,称为引入了切分脆弱性作为分形维数与平均节点度之间的比率,并研究了它与断开网络所需的随机移除的管道数量以及某些拓扑度量之间的关系。分析表明,新索引在描述WDS的全球脆弱性方面是有效的。

更新日期:2021-03-15
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