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Graph Neural Networks (GNNs) have achieved promising results in tasks such as node classification and graph classification. However, recent studies reveal that GNNs are vulnerable to backdoor attacks, posing a significant threat to their…

Machine Learning · Computer Science 2025-03-13 Zhiwei Zhang , Minhua Lin , Junjie Xu , Zongyu Wu , Enyan Dai , Suhang Wang

Recent studies have shown that graph neural networks (GNNs) are vulnerable to adversarial attacks, posing significant challenges to their deployment in safety-critical scenarios. This vulnerability has spurred a growing focus on designing…

Machine Learning · Computer Science 2025-05-27 Tao Wu , Canyixing Cui , Xingping Xian , Shaojie Qiao , Chao Wang , Lin Yuan , Shui Yu

Extensive researches have been dedicated to investigating the performance of real networks and synthetic networks against random failures or intentional attack guided by degree (degree attack). Degree is one of straightforward measures to…

Physics and Society · Physics 2011-09-26 Hui Wang , Jinyuan Huang , Xiaomin Xu , Yanghua Xiao , Wei Wang

We examine two properties of complex networks, the robustness against targeted node removal (attack) and the transport efficiency in terms of degree correlation in node connection by numerical evaluation of exact analytic expressions. We…

Physics and Society · Physics 2012-09-25 Toshihiro Tanizawa

We study a graph-theoretic property known as robustness, which plays a key role in certain classes of dynamics on networks (such as resilient consensus, contagion and bootstrap percolation). This property is stronger than other graph…

Social and Information Networks · Computer Science 2015-03-20 Haotian Zhang , Elaheh Fata , Shreyas Sundaram

The robustness of complex networks against node failure and malicious attack has been of interest for decades, while most of the research has focused on random attack or hub-targeted attack. In many real-world scenarios, however, attacks…

Physics and Society · Physics 2015-06-23 Shuai Shao , Xuqing Huang , H Eugene Stanley , Shlomo Havlin

In recent years, the notion of r-robustness for the communication graph of the network has been introduced to address the challenge of achieving consensus in the presence of misbehaving agents. Higher r-robustness typically implies higher…

Systems and Control · Electrical Eng. & Systems 2025-04-14 Haejoon Lee , Dimitra Panagou

With increasingly ambitious initiatives such as GENI and FIND that seek to design the future Internet, it becomes imperative to define the characteristics of robust topologies, and build future networks optimized for robustness. This paper…

Networking and Internet Architecture · Computer Science 2009-09-25 Ali Sydney , Caterina Scoglio , Mina Youssef , Phillip Schumm

We model the robustness against random failure or intentional attack of networks with arbitrary large-scale structure. We construct a block-based model which incorporates --- in a general fashion --- both connectivity and interdependence…

Physics and Society · Physics 2012-09-25 Tiago P. Peixoto , Stefan Bornholdt

Much of our commerce and traveling depend on the efficient operation of large scale networks. Some of those, such as electric power grids, transportation systems, communication networks, and others, must maintain their efficiency even after…

Physics and Society · Physics 2015-03-26 Vitor H. P. Louzada , Fabio Daolio , Hans J. Herrmann , Marco Tomassini

We study the response of complex networks subject to attacks on vertices and edges. Several existing complex network models as well as real-world networks of scientific collaborations and Internet traffic are numerically investigated, and…

Disordered Systems and Neural Networks · Physics 2009-11-07 Petter Holme , Beom Jun Kim , Chang No Yoon , Seung Kee Han

Despite the exploding interest in graph neural networks there has been little effort to verify and improve their robustness. This is even more alarming given recent findings showing that they are extremely vulnerable to adversarial attacks…

Machine Learning · Computer Science 2019-12-20 Aleksandar Bojchevski , Stephan Günnemann

Previous studies on the invulnerability of scale-free networks under edge attacks supported the conclusion that scale-free networks would be fragile under selective attacks. However, these studies are based on qualitative methods with…

Social and Information Networks · Computer Science 2012-11-15 Bojin Zheng , Hongrun Wu , Wenhua Du , Wanneng Shu , Jun Qin

Deep learning is vulnerable to adversarial examples. Many defenses based on randomized neural networks have been proposed to solve the problem, but fail to achieve robustness against attacks using proxy gradients such as the Expectation…

Machine Learning · Computer Science 2021-07-07 Sungyoon Lee , Hoki Kim , Jaewook Lee

Finding graph indices which are unbiased to network size and density is of high importance both within a given field and across fields for enhancing comparability of modern network science studies. The degree variance is an important metric…

Social and Information Networks · Computer Science 2021-01-26 Keith M. Smith , Javier Escudero

Network controllability robustness reflects how well a networked dynamical system can maintain its controllability against destructive attacks. This paper investigates the network controllability robustness from the perspective of a…

Physics and Society · Physics 2021-03-09 Yang Lou , Lin Wang , Guanrong Chen

Graphs are pervasive in our everyday lives, with relevance to biology, the internet, and infrastructure, as well as numerous other applications. It is thus necessary to have an understanding as to how quickly a graph disintegrates, whether…

Social and Information Networks · Computer Science 2025-12-25 Jeremie Fish , Mahesh Banavar , Erik Bollt

In this paper, robustness of planar trivalent random graphs to targeted attacks of highest connected nodes is investigated using numerical simulations. It is shown that these graphs are relatively robust. The nonrandom node removal process…

Statistical Mechanics · Physics 2009-11-13 J. -P. Kownacki

Generally, networks are classified into two sides of inequality and equality with respect to the number of links at nodes by the types of degree distributions. One side includes many social, technological, and biological networks which…

Physics and Society · Physics 2025-10-01 Yukio Hayashi , Taishi Ogawa

Robustness against adversarial attack in neural networks is an important research topic in the machine learning community. We observe one major source of vulnerability of neural nets is from overparameterized fully-connected layers. In this…

Machine Learning · Computer Science 2021-02-01 Bingyuan Liu , Christopher Malon , Lingzhou Xue , Erik Kruus