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Complex systems are characterized by many interacting units that give rise to emergent behavior. A particularly advantageous way to study these systems is through the analysis of the networks that encode the interactions among the system's…

Physics and Society · Physics 2019-03-21 Alberto Aleta , Yamir Moreno

The reliable and resilient operation of the smart grid necessitates a clear understanding of the intra-and-inter dependencies of its power and communication systems. This understanding can only be achieved by accurately depicting the…

Networking and Internet Architecture · Computer Science 2020-08-03 Sohini Roy , Harish Chandrasekaran , Anamitra Pal , Arunabha Sen

We present two different approaches to model power grids as interconnected networks of networks. Both models are derived from a model for spatially embedded mono-layer networks and are generalised to handle an arbitrary number of network…

Physics and Society · Physics 2017-01-25 Paul Schultz , Frank Hellmann , Jobst Heitzig , Jürgen Kurths

Modern network-like systems are usually coupled in such a way that failures in one network can affect the entire system. In infrastructures, biology, sociology, and economy, systems are interconnected and events taking place in one system…

Data Analysis, Statistics and Probability · Physics 2010-12-02 S. Havlin , N. A. M. Araujo , S. V. Buldyrev , C. S. Dias , R. Parshani , G. Paul , H. E. Stanley

Multilayer network science has emerged as a central framework for analysing interconnected and interdependent complex systems. Its relevance has grown substantially with the increasing availability of rich, heterogeneous data, which makes…

Modern networks are becoming increasingly interdependent. As a prominent example, the smart grid is an electrical grid controlled through a communications network, which in turn is powered by the electrical grid. Such interdependencies…

Networking and Internet Architecture · Computer Science 2016-11-17 Agostino Sturaro , Simone Silvestri , Mauro Conti , Sajal K. Das

In the real world, the stable operation of a network is usually inseparable from the mutual support of other networks. In such an interdependent network, a node in one layer may depend on multiple nodes in another layer, forming a complex…

Social and Information Networks · Computer Science 2025-09-30 Cheng Qian , Dandan Zhao , Bo Zhang , Ming Zhong , Jianmin Han , Shenghong Li , Hao Peng , Wei Wang

Networked structures arise in a wide array of different contexts such as technological and transportation infrastructures, social phenomena, and biological systems. These highly interconnected systems have recently been the focus of a great…

Statistical Mechanics · Physics 2009-11-10 Alain Barrat , Marc Barthelemy , Romualdo Pastor-Satorras , Alessandro Vespignani

The rapid advancement of technology underscores the critical importance of robustness in complex network systems. This paper presents a framework for investigating the structural robustness of interconnected network models. This paper…

Physics and Society · Physics 2023-11-01 Dong Gaogao , Sun Nannan , Wang Fan

The study of complex networks has been historically based on simple graph data models representing relationships between individuals. However, often reality cannot be accurately captured by a flat graph model. This has led to the…

Social and Information Networks · Computer Science 2013-03-21 Matteo Magnani , Barbora Micenkova , Luca Rossi

Understanding and characterizing the vulnerability of urban infrastructures, which refers to the engineering facilities essential for the regular running of cities and that exist naturally in the form of networks, is of great value to us.…

Machine Learning · Computer Science 2023-08-02 Jinzhu Mao , Liu Cao , Chen Gao , Huandong Wang , Hangyu Fan , Depeng Jin , Yong Li

Most real-world complex systems can be modelled by coupled networks with multiple layers. How and to what extent the pattern of couplings between network layers may influence the interlaced structure and function of coupled networks are not…

Data Analysis, Statistics and Probability · Physics 2010-10-26 Won-kuk Cho , K. -I. Goh , I. -M. Kim

The electric power grid is a critical societal resource connecting multiple infrastructural domains such as agriculture, transportation, and manufacturing. The electrical grid as an infrastructure is shaped by human activity and public…

Critical Infrastructures like power and communication networks are highly interdependent on each other for their full functionality. Many significant research have been pursued to model the interdependency and failure analysis of these…

Networking and Internet Architecture · Computer Science 2017-02-06 Joydeep Banerjee , Chenyang Zhou , Arunabha Sen

A realistic communication system model is critical in power system studies emphasizing the cyber and physical intercoupling. In this paper, we provide characteristics that could be used in modeling the underlying cyber network for power…

Systems and Control · Electrical Eng. & Systems 2021-03-03 Morayo Soetan , Zeyu Mao , Katherine Davis

Robustness of network of networks (NON) has been studied only for dependency coupling (J.X. Gao et. al., Nature Physics, 2012) and only for connectivity coupling (E.A. Leicht and R.M. D Souza, arxiv:0907.0894). The case of network of n…

Physics and Society · Physics 2013-10-22 Gaogao Dong , Lixin Tian , Ruijin Du , H. Eugene Stanley

Interconnected networks describe the dynamics of important systems in a wide range such as biological systems and electrical power grids. Some important features of these systems were successfully studied and understood through simplified…

Systems and Control · Computer Science 2016-03-18 Thanh Long Vu , Konstantin Turitsyn

Power lines, roadways, pipelines and other physical infrastructure are critical to modern society. These structures may be viewed as spatial networks where geographic distances play a role in the functionality and construction cost of…

Physics and Society · Physics 2015-06-03 Thomas C. McAndrew , Christopher M. Danforth , James P. Bagrow

This paper presents an unusual view of interference wireless networks based on complex system thinking. To proceed with this analysis, a literature review of the different applications of complex systems is firstly presented to illustrate…

Information Theory · Computer Science 2013-03-13 Pedro H. J. Nardelli , Paulo Cardieri , William A. Kretzschmar , Matti Latva-aho

Power systems are subject to fundamental changes due to the increasing infeed of decentralised renewable energy sources and storage. The decentralised nature of the new actors in the system requires new concepts for structuring the power…

Adaptation and Self-Organizing Systems · Physics 2020-04-22 Lia Strenge , Paul Schultz , Jürgen Kurths , Jörg Raisch , Frank Hellmann