Percolation on complex networks: Theory and application

Li, Ming; Liu, Run-Ran; Lü, Linyuan; Hu, Mao-Bin; Xu, Shuqi; Zhang, Yicheng

doi:10.1016/j.physrep.2020.12.003

Cited by 224 publications

(104 citation statements)

References 485 publications

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“…[53,55] considered partially tolerated interdependence among layers. As Li et al [16] mentioned, the combination of tolerated and correlated interdependency was studied in [56] which was not among the papers collected in this study. In this case, different tolerances were assigned to dependency links according to their degree correlation.…”

Section: F Form Of Interdependencementioning

confidence: 93%

“…These definitions are close to the theoretical approach of the percolation theory to study the behavior of networks when some nodes and links are designated as removed [16][17]. It can be the reason why the percolation theory is the most popular in studying and analyzing the robustness of networked systems [18].…”

Section: Introductionmentioning

confidence: 93%

“…Four databases including Scopus, Web of Science, Google Scholars, and Cochran were searched to find other similar review papers based on the applied inclusion/exclusion criteria of this study. Only five review articles turned up [16,[20][21][22]34], yet none of them was a systematic review. In more detail, they did not contain the paper selection criteria and data processing.…”

Section: A Planning the Reviewmentioning

confidence: 99%

“…It can be the reason why the percolation theory is the most popular in studying and analyzing the robustness of networked systems [18]. The percolation theory is to study the behavior of networks in terms of the critical percolation threshold and the size of the giant component, when some nodes and links are assigned as removed [16,17]. In percolation theory, the removal fraction of nodes/links is tuned increasingly from zero to a certain critical threshold in which the state of the network shifts from connected to disconnected according to the decreasing size of the giant connected components [19].…”

Section: Introductionmentioning

confidence: 99%

“…However, many studies related to percolation theory have been focused on single-layer networks while real-world systems, including infrastructure systems, are composed of multilayer networks [20]. Applying percolation theory for analyzing multilayer networks was initiated by Buldyrev et al [14] in 2010 [16,20,21]. They utilized the percolation approach to study the robustness in a 2-layer network by defining two types of links; (i) connectivity links that connect nodes within layers and (ii) dependency links that connect nodes between layers.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Network Properties for Robust Multilayer Infrastructure Systems: A Percolation Theory Review

2021

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Infrastructure systems, such as power, transportation, telecommunication, and water systems, are composed of multiple components which are interconnected and interdependent to produce and distribute essential goods and services. So, the robustness of infrastructure systems to resist disturbances is critical for the durable performance of modern societies. Multilayer networks have been used to model the multiplicity and interrelation of infrastructure systems and percolation theory is the most common approach to quantify the robustness of such networks. This survey systematically reviews literature published between 2010 and 2021, on applying percolation theory to assess the robustness of infrastructure systems modeled as multilayer networks. We discussed all network properties applied to build infrastructure models. Among all properties, interdependency strength and communities were the most common network property whilst very few studies considered realistic attributes of infrastructure systems such as directed links and feedback conditions. The review highlights that the properties produced approximately similar model outcomes, in terms of detecting improvement or deterioration in the robustness of multilayer infrastructure networks, with few exceptions. Most of the studies focused on highly simplified synthetic models rather than models built by real datasets. Thus, this review suggests analyzing multiple properties in a single model to assess whether they boost or weaken the impact of each other. In addition, the effect size of different properties on the robustness of infrastructure systems should be quantified. It can support the design and planning of robust infrastructure systems by arranging and prioritizing the most effective properties.

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Section: F Form Of Interdependencementioning

confidence: 93%

Section: Introductionmentioning

confidence: 93%

Section: A Planning the Reviewmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Network Properties for Robust Multilayer Infrastructure Systems: A Percolation Theory Review

2021

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Percolation behavior and sensing performance of polypropylene‐based conductive polymer composites under compressive strains and temperature

Wu,

Xie,

Shao

et al. 2024

Journal of Polymer Science

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Percolation behavior is highly significant for mechanical, thermal, and electrical properties, as well as manufacturing processes of conductive polymer composites (CPCs). It has been reported that temperature and external loads are important parameters directly affecting the percolation threshold. Herein, carbon black/polypropylene (CB/PP) and carbon black/multiwalled carbon nanotubes/polypropylene (CB/MWCNTs/PP) composites are prepared via the melt blending method. After the synthesis of composites, the rheological properties, the filler distribution, crystallization, and conductive network formation within the composite are evaluated. The effect of conductive network structure on conductive percolation behavior is studied under various compressive strains and temperatures. Finally, the sensing performance under compressive strain and temperature cycling is discussed. Obtained results reveal that MWCNTs work as “bridges” between segregated CB particles leading to a synergic effect on the conducting properties. The volume resistivity of PP‐based CPCs exhibits a critical strain and a positive temperature coefficient (PTC), resulting in altered percolation. PP‐based CPCs with the addition of MWCNTs have greater PTC intensity, demonstrating sensing stability and sensitivity to compressive strain under temperature cycling. This study underscores the essential contribution of MWCNTs in building conductive networks and elucidates the potential application of PP‐based CPCs with superior sensing performance under compressive strain and varying temperatures.

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A novel vulnerability measure based on complex network communities

Jouyban,

Hosseini

2024

Softw Pract Exp

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This article introduces a novel vulnerability measure, based on the structure of complex network communities, to assess the significance and security of network communities, influencing complex network security, connectivity, and the prevention of cascading failures. Initially, the spectral clustering algorithm is applied to identify the communities of complex networks. Determining the appropriate number of communities is crucial in the proposed vulnerability measure and security approach. The number of communities is estimated based on the characteristics of the normalized Laplace matrix within the algorithm. Subsequently, leveraging the community structure, a vulnerability measure is proposed for community evaluation by considering three aspects of internal criteria, external criteria and node location criterion. Weight parameters are also incorporated to customize the measure according to the importance of each factor in varying security scenarios. Finally, the effectiveness of the proposed vulnerability measure as a security strategy is evaluated on ten real‐world complex networks from different categories. The experimental results demonstrate the effectiveness and efficiency of the proposed measure in assessing community vulnerability and consequently using appropriate maps and policies for the complex network security.

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Percolation on complex networks: Theory and application

Cited by 224 publications

References 485 publications

Network Properties for Robust Multilayer Infrastructure Systems: A Percolation Theory Review

Network Properties for Robust Multilayer Infrastructure Systems: A Percolation Theory Review

Percolation behavior and sensing performance of polypropylene‐based conductive polymer composites under compressive strains and temperature

A novel vulnerability measure based on complex network communities

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