幂律网络不完全连接结构上相互依赖关系的建模

G. Weldehawaryat, S. Wolthusen
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引用次数: 2

摘要

关键基础设施,特别是信息和电信网络、系统和电力网络之间的相互依存关系,已经采用许多不同的方法进行了深入研究,从半定性莱昂惕夫模型到渗透模型,以及从统计物理学到代理和图理论模型的相关方法。本文主要讨论后一种方法,并研究两个幂律网络不完全连接所产生的结构。ICT和电力网络都是人工网络,但许多研究表明,这些网络通常具有无标度特性,可以用幂律度序列图高精度地描述。一个众所周知的结果是,这些网络对随机故障和故意攻击的稳健性差异很大,对目标攻击的脆弱性很高。然而,基于精确度序列的鲁棒性存在差异。两个或更多这样的网络之间的依赖关系可能导致两种依赖路径,其中路径的长度以及顶点和边缘不相交路径的存在可以为缓解机制提供信息;然而,更重要的是,周期的出现表明相互依赖关系的存在,这种相互依赖关系可能更难以恢复或减轻。这已经在之前的简单图和流中进行了研究;然而,我们认为,特别是对于智能电网环境中电力和ICT网络之间(相互)依赖的情况,图表之间的这种关系本身并不是静态的。我们以稀疏随机图的形式考虑依赖关系的存在、添加或去除,从而产生相互依赖循环。这种循环的直径可以作为整个网络脆弱性的一个强有力的指标,因为它可以指示网络的攻击面。在图中引入额外的边,表明智能电网中的信息流,因此可以减少漏洞,因此在给定图中有效地发现这种结构是特别有趣的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Modelling interdependencies over incomplete join structures of power law networks
The interdependence of critical infrastructures, particularly of information and telecommunication networks and systems and electrical power networks has been studied intensively employing a number of different methods ranging from semi-qualitative Leontief models via percolation models and related approaches from statistical physics to agent and graph-theoretical models. In this paper we focus on the latter approach and study the structures arising from incomplete joining of two power-law networks. Both ICT and power networks are artificial networks, but a number of studies demonstrate that such networks generally exhibit scale-free properties and can be described with high accuracy by power-law degree sequence graphs. A well-known result is that the robustness of such networks to random failures and intentional attack differs considerably, with high levels of vulnerability to targeted attacks. However, differences in robustness exist based on the exact degree sequence. Dependencies between two or more such networks can result in both dependency paths, where the length of paths and the existence of vertex-and edge-disjoint paths can inform mitigation mechanisms; more importantly, however, cycles arising indicate the existence of interdependencies that may be more difficult to recover from or mitigate. This has been studied previously for both simple graphs and for flows; however, we argue that particularly for the case of (inter-)dependencies between power and ICT networks in smart grid environments, this relation between the graphs is itself not static. We consider the existence, addition, or removal of dependencies in the form of sparse random graphs resulting in the creation of interdependence cycles. The diameter of such cycles can serve as a strong indicator of the vulnerability of the overall network as it is indicative of the attack surface of the network. The introduction of additional edges in the graph, indicating information flows in the smart grid, can hence reduce vulnerabilities, hence the efficient discovery of such structures for a given graph is of particular interest.
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