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Modeling how networks change under structural perturbations can yield foundational insights into network robustness, which is critical in many real-world applications. The largest connected component is a popular measure of network…

Physics and Society · Physics 2025-09-30 Jessica Jiang , Allison C. Zhuang , Petter Holme , Peter J. Mucha , Alice C. Schwarze

An input-output approach to stability analysis is explored for networked systems with uncertain link dynamics. The main result consists of a collection of integral quadratic constraints, which together imply robust stability of the…

Systems and Control · Electrical Eng. & Systems 2024-11-22 Simone Mariano , Michael Cantoni

Modern world builds on the resilience of interdependent infrastructures characterized as complex networks. Recently, a framework for analysis of interdependent networks has been developed to explain the mechanism of resilience in…

Physics and Society · Physics 2015-06-16 Peng Zhang , Baisong Cheng , Zhuang Zhao , Daqing Li , Guangquan Lu , Yunpeng Wang , Jinghua Xiao

An input-output model for networks with link uncertainty is developed. The main result presents a set of integral quadratic constraints (IQCs) that collectively imply robust stability of the uncertain network dynamics. The model dependency…

Systems and Control · Electrical Eng. & Systems 2025-12-25 Simone Mariano , Chung-Yao Kao , Michael Cantoni

Models of street networks underlie research in urban travel behavior, accessibility, design patterns, and morphology. These models are commonly defined as planar, meaning they can be represented in two dimensions without any underpasses or…

Physics and Society · Physics 2018-11-21 Geoff Boeing

Transportation networks serve as windows into the complex world of urban systems. By properly characterizing a road network, we can therefore better understand its encompassing urban system. This study offers a geometrical approach towards…

Physics and Society · Physics 2015-07-15 Farideddin Peiravian , Sybil Derrible

Despite recent progress in reducing road fatalities, the persistently high rate of traffic-related deaths highlights the necessity for improved safety interventions. Leveraging large-scale graph-based nationwide road network data across 49…

Machine Learning · Computer Science 2024-11-06 Xiwen Chen , Sayed Pedram Haeri Boroujeni , Xin Shu , Huayu Li , Abolfazl Razi

This paper introduces a traffic evacuation model for railway disruptions to improve resilience. The research focuses on the problem of failure of several nodes or lines on the railway network topology. We proposed a holistic approach that…

Numerical Analysis · Mathematics 2025-03-10 Hangli Ge , Xiaojie Yang , Jinyu Chen , Francesco Flammini , Noboru Koshizuka

We study properties of Graph Convolutional Networks (GCNs) by analyzing their behavior on standard models of random graphs, where nodes are represented by random latent variables and edges are drawn according to a similarity kernel. This…

Machine Learning · Statistics 2020-10-26 Nicolas Keriven , Alberto Bietti , Samuel Vaiter

Research on the robustness of the Internet has gained critical importance in the last decades because more and more individuals, societies and firms rely on this global network infrastructure for communication, knowledge transfer, business…

Networking and Internet Architecture · Computer Science 2021-03-10 Milena Oehlers , Benjamin Fabian

Graph convolutional neural networks (GCNNs) have emerged as powerful tools for analyzing graph-structured data, achieving remarkable success across diverse applications. However, the theoretical understanding of the stability of these…

Machine Learning · Computer Science 2025-10-28 Ning Zhang , Henry Kenlay , Li Zhang , Mihai Cucuringu , Xiaowen Dong

A unified approach to studying convergence and stochastic stability of continuous time consensus protocols (CPs) is presented in this work. Our method applies to networks with directed information flow; both cooperative and noncooperative…

Optimization and Control · Mathematics 2012-06-05 Georgi S. Medvedev

This paper studies the observability radius of network systems, which measures the robustness of a network to perturbations of the edges. We consider linear networks, where the dynamics are described by a weighted adjacency matrix, and…

Systems and Control · Computer Science 2016-12-20 Gianluca Bianchin , Paolo Frasca , Andrea Gasparri , Fabio Pasqualetti

The Transmission Control Protocol (TCP) utilizes congestion avoidance and control mechanisms as a preventive measure against congestive collapse and as an adaptive measure in the presence of changing network conditions. The set of available…

Networking and Internet Architecture · Computer Science 2022-04-27 Gayane Vardoyan , C. V. Hollot , Don Towsley

We present a comparative network theoretic analysis of the two largest global transportation networks: The worldwide air-transportation network (WAN) and the global cargoship network (GCSN). We show that both networks exhibit striking…

Physics and Society · Physics 2011-03-29 Grastivia O'Danleyman , Jake Jungbin Lee , Hanno Seebens , Bernd Blasius , Dirk Brockmann

In this paper we propose an alternative approach for the assessment of network vulnerability under random and intentional attacks as compared to the results obtained from the "vulnerability function" given by Criado et al. [Criado et al.…

Computational Physics · Physics 2011-01-12 A. Yazdani , P. Jeffrey

This paper proposes a comparison between rectilinear and radio-concentric networks. Indeed, those networks are often observed in urban areas, in several cities all over the world. One of the interesting properties of such networks is…

Social and Information Networks · Computer Science 2016-09-20 Didier Josselin , Vincent Labatut , Dieter Mitsche

In this work, we have proposed a system theoretic method to compute sensitivities of different lines for $N-k$ contingency analysis in power network. We have formulated the $N-k$ contingency analysis as the stability problem of power…

Optimization and Control · Mathematics 2018-01-03 Sambarta Dasgupta , Umesh Vaidya

With a simple model, we study the evolution of random networks under attack and reconstruction. We introduce a new quality, invulnerability I(s), to describe the stability of the system. We find that the network can evolve to a stationary…

Disordered Systems and Neural Networks · Physics 2007-05-23 L. P. Chi , C. B. Yang , X. Cai

Resilience of cyber-physical networks to unexpected failures is a critical need widely recognized across domains. For instance, power grids, telecommunication networks, transportation infrastructures and water treatment systems have all…

Systems and Control · Electrical Eng. & Systems 2024-02-19 Jean-Baptiste Bouvier , Sai Pushpak Nandanoori , Melkior Ornik