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Robustness and Resilience of Complex Networks

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Complexity".

Deadline for manuscript submissions: 30 April 2025 | Viewed by 3244

Special Issue Editors


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Guest Editor
Department of Industrial Engineering, University of Trento, 9 Via Sommarive, 38123 Trento, Italy
Interests: complex systems; emergence; dynamical systems; system robustness; critical transitions; systems biology; mathematical epidemiology

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Guest Editor
CNR, Institute of Complex Systems, Via Madonna del Piano 10, 50019 Sesto Fiorentino, FI, Italy
Interests: pattern formation and competition; nonlinear dynamics; complex networks; synchronization; complex systems

Special Issue Information

Dear Colleagues,

This Special Issue promotes interdisciplinary research and looks into the topic of robustness and resilience for complex systems and networks. This translational topic, which is strongly emerging in pure and applied research, calls for multifaceted approaches, integrating techniques from network theory, control engineering, information theory, and more, as well as applied research from single disciplines like ecology, physics, engineering, management, and so forth.

Natural and artificial systems and networks often share the capability to maintain critical functions and properties despite uncertainties, fluctuations, and perturbations, both in their topology and in their dynamics. Multidisciplinary endeavors are dedicated to unraveling the key characteristics, such as structural, mechanical, and dynamical, that guarantee such behavior, to developing comprehensive frameworks to study it, and to detecting and anticipating losses of robustness and resilience. Additional research avenues in the direction of management and control are also warranted.

We thus ask for contributions around this thrilling topic, both theoretical and applied, in order to frame a comprehensive picture of the quantitative theories and techniques to address the question of dynamical networks persisting in their functions despite alterations.

We thus call for original research papers and comprehensive reviews about, but not limited to, the following topics:

  • Investigation of network robustness (in network theory sense) against topological alterations;
  • Investigation of system robustness (in control sense) under parametric uncertainties;
  • Modeling of system and network resilience, i.e., persistence of function despite uncertainties and perturbations;
  • Multidisciplinary contributions on the framework of robustness and resilience, employing methods from mathematics, bifurcation theory, information theory, and more;
  • Development and performance assessment of indicators for resilience loss, both model- and data-driven;
  • Advances in detection and anticipation of tipping points in complex networks, both model-based and data-driven;
  • Cross-fertilization between the fields of system robustness and critical transitions;
  • Suggestions for control of fragile and hysteretic systems;
  • Advanced computational algorithms in real problems;
  • Domain-specific applications, employing models or empirical data.

Dr. Daniele Proverbio
Dr. Stefano Boccaletti
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • networks
  • robustness
  • resilience
  • complex systems
  • systems biology
  • engineering
  • control theory
  • ecology
  • management science
  • information theory
  • bifurcations
  • non-equilibrium
  • early warning signals
  • tipping points
  • monotone systems

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Published Papers (3 papers)

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Research

31 pages, 1865 KiB  
Article
Robustness Analysis of Multilayer Infrastructure Networks Based on Incomplete Information Stackelberg Game: Considering Cascading Failures
by Haitao Li, Lixin Ji, Yingle Li and Shuxin Liu
Entropy 2024, 26(11), 976; https://doi.org/10.3390/e26110976 - 14 Nov 2024
Viewed by 407
Abstract
The growing importance of critical infrastructure systems (CIS) makes maintaining their normal operation against deliberate attacks such as terrorism a significant challenge. Combining game theory and complex network theory provides a framework for analyzing CIS robustness in adversarial scenarios. Most existing studies focus [...] Read more.
The growing importance of critical infrastructure systems (CIS) makes maintaining their normal operation against deliberate attacks such as terrorism a significant challenge. Combining game theory and complex network theory provides a framework for analyzing CIS robustness in adversarial scenarios. Most existing studies focus on single-layer networks, while CIS are better modeled as multilayer networks. Research on multilayer network games is limited, lacking methods for constructing incomplete information through link hiding and neglecting the impact of cascading failures. We propose a multilayer network Stackelberg game model with incomplete information considering cascading failures (MSGM-IICF). First, we describe the multilayer network model and define the multilayer node-weighted degree. Then, we present link hiding rules and a cascading failure model. Finally, we construct MSGM-IICF, providing methods for calculating payoff functions from the different perspectives of attackers and defenders. Experiments on synthetic and real-world networks demonstrate that link hiding improves network robustness without considering cascading failures. However, when cascading failures are considered, they become the primary factor determining network robustness. Dynamic capacity allocation enhances network robustness, while changes in dynamic costs make the network more vulnerable. The proposed method provides a new way of analyzing the robustness of diverse CIS, supporting resilient CIS design. Full article
(This article belongs to the Special Issue Robustness and Resilience of Complex Networks)
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17 pages, 736 KiB  
Article
Functional Hypergraphs of Stock Markets
by Jerry Jones David, Narayan G. Sabhahit, Sebastiano Stramaglia, T. Di Matteo, Stefano Boccaletti and Sarika Jalan
Entropy 2024, 26(10), 848; https://doi.org/10.3390/e26100848 - 8 Oct 2024
Viewed by 1601
Abstract
In stock markets, nonlinear interdependencies between various companies result in nontrivial time-varying patterns in stock prices. A network representation of these interdependencies has been successful in identifying and understanding hidden signals before major events like stock market crashes. However, these studies have revolved [...] Read more.
In stock markets, nonlinear interdependencies between various companies result in nontrivial time-varying patterns in stock prices. A network representation of these interdependencies has been successful in identifying and understanding hidden signals before major events like stock market crashes. However, these studies have revolved around the assumption that correlations are mediated in a pairwise manner, whereas, in a system as intricate as this, the interactions need not be limited to pairwise only. Here, we introduce a general methodology using information-theoretic tools to construct a higher-order representation of the stock market data, which we call functional hypergraphs. This framework enables us to examine stock market events by analyzing the following functional hypergraph quantities: Forman–Ricci curvature, von Neumann entropy, and eigenvector centrality. We compare the corresponding quantities of networks and hypergraphs to analyze the evolution of both structures and observe features like robustness towards events like crashes during the course of a time period. Full article
(This article belongs to the Special Issue Robustness and Resilience of Complex Networks)
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17 pages, 1690 KiB  
Article
Robust Optimization Research of Cyber–Physical Power System Considering Wind Power Uncertainty and Coupled Relationship
by Jiuling Dong, Zilong Song, Yuanshuo Zheng, Jingtang Luo, Min Zhang, Xiaolong Yang and Hongbing Ma
Entropy 2024, 26(9), 795; https://doi.org/10.3390/e26090795 - 17 Sep 2024
Viewed by 700
Abstract
To mitigate the impact of wind power uncertainty and power–communication coupling on the robustness of a new power system, a bi-level mixed-integer robust optimization strategy is proposed. Firstly, a coupled network model is constructed based on complex network theory, taking into account the [...] Read more.
To mitigate the impact of wind power uncertainty and power–communication coupling on the robustness of a new power system, a bi-level mixed-integer robust optimization strategy is proposed. Firstly, a coupled network model is constructed based on complex network theory, taking into account the coupled relationship of energy supply and control dependencies between the power and communication networks. Next, a bi-level mixed-integer robust optimization model is developed to improve power system resilience, incorporating constraints related to the coupling strength, electrical characteristics, and traffic characteristics of the information network. The upper-level model seeks to minimize load shedding by optimizing DC power flow using fuzzy chance constraints, thereby reducing the risk of power imbalances caused by random fluctuations in wind power generation. Furthermore, the deterministic power balance constraints are relaxed into inequality constraints that account for wind power forecasting errors through fuzzy variables. The lower-level model focuses on minimizing traffic load shedding by establishing a topology–function-constrained information network traffic model based on the maximum flow principle in graph theory, thereby improving the efficiency of network flow transmission. Finally, a modified IEEE 39-bus test system with intermittent wind power is used as a case study. Random attack simulations demonstrate that, under the highest link failure rate and wind power penetration, Model 2 outperforms Model 1 by reducing the load loss ratio by 23.6% and improving the node survival ratio by 5.3%. Full article
(This article belongs to the Special Issue Robustness and Resilience of Complex Networks)
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