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In many systems consisting of interacting subsystems, the complex interactions between elements can be represented using multilayer networks. However percolation, key to understanding connectivity and robustness, is not trivially…

Disordered Systems and Neural Networks · Physics 2020-11-04 G. J. Baxter , R. A. da Costa , S. N. Dorogovtsev , J. F. F. Mendes

Modern large network systems normally work in cooperation and incorporate dependencies between their components for purposes of efficiency and regulation. Such dependencies may become a major risk since they can cause small scale failures…

Physics and Society · Physics 2020-08-12 Dong Zhou , Amir Bashan

Multilayer networks have been found to be prone to abrupt cascading failures under random and targeted attacks, but most of the targeting algorithms proposed so far have been mainly tested on uncorrelated systems. Here we show that the size…

Physics and Society · Physics 2020-07-23 Andrea Santoro , Vincenzo Nicosia

Real-world complex systems always interact with each other, which causes these systems to collapse in an avalanche or cascading manner in the case of random failures or malicious attacks. The robustness of multilayer networks has attracted…

Physics and Society · Physics 2019-11-14 Wen-Jun Jiang , Run-Ran Liu , Chun-Xiao Jia

We consider a class of random, weighted networks, obtained through a redefinition of patterns in an Hopfield-like model and, by performing percolation processes, we get information about topology and resilience properties of the networks…

Statistical Mechanics · Physics 2015-05-30 Elena Agliari , Claudia Cioli , Enore Guadagnini

We analyze the stability of the network's giant connected component under impact of adverse events, which we model through the link percolation. Specifically, we quantify the extent to which the largest connected component of a network…

The existence of inter-dependence between multiple networks imparts an additional scale of complexity to such systems often referred to as `network of networks' (NON). We have investigated the robustness of NONs to random breakdown of their…

Physics and Society · Physics 2019-01-09 Aradhana Singh , Sitabhra Sinha

We study the effects of nonreciprocity and network structure on percolation. To this end, we investigate nonreciprocal random networks - directed networks for which the probability of a link occurring from node i to node j differs from the…

Statistical Mechanics · Physics 2025-10-07 Chanania Steinbock

We examine the structure of the percolating cluster (PC) formed by site percolation on a random clustered network (RCN) model. Using the generating functions, we formulate the clustering coefficient and assortative coefficient of the PC. We…

Physics and Society · Physics 2020-06-23 Takehisa Hasegawa , Shogo Mizutaka

For interdependent networks with identity dependency map, percolation is exactly the same with that on a single network and follows a second-order phase transition, while for random dependency, percolation follows a first-order phase…

Social and Information Networks · Computer Science 2016-02-17 Jing Yuan , Lixiang Li , Haipeng Peng , Jürgen Kurths , Xiaojing Hua , Yixian Yang

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

Interdependent networks are characterized by two kinds of interactions: The usual connectivity links within each network and the dependency links coupling nodes of different networks. Due to the latter links such networks are known to…

Physics and Society · Physics 2015-06-18 Marcell Stippinger , János Kertész

The functionality of an entity frequently necessitates the support of a group situated in another layer of the system. To unravel the profound impact of such group support on a system's resilience against cascading failures, we devise a…

Physics and Society · Physics 2024-08-05 Lei Chen , Chunxiao Jia , Run-Ran Liu , Fanyuan Meng

The function of a real network depends not only on the reliability of its own components, but is affected also by the simultaneous operation of other real networks coupled with it. Robustness of systems composed of interdependent network…

Physics and Society · Physics 2015-07-10 Filippo Radicchi

The emergence and evolution of real-world systems have been extensively studied in the last few years. However, equally important phenomena are related to the dynamics of systems' collapse, which has been less explored, especially when they…

Physics and Society · Physics 2019-09-27 Jie Li , Chengyi Xia , Gaoxi Xiao , Yamir Moreno

Given a connected network, it can be augmented by applying a growing strategy (e.g. random or scale-free rules) over the previously existing structure. Another approach for augmentation, recently introduced, involves incorporating a direct…

Statistical Mechanics · Physics 2007-05-23 Luciano da Fontoura Costa

From transportation networks to complex infrastructures, and to social and communication networks, a large variety of systems can be described in terms of multiplexes formed by a set of nodes interacting through different networks (layers).…

Statistical Mechanics · Physics 2015-06-16 Davide Cellai , Eduardo López , Jie Zhou , James P. Gleeson , Ginestra Bianconi

The study of interdependent networks, and in particular the robustness on networks, has attracted considerable attention. Recent studies mainly assume that the dependence is fully interdependent. However, targeted attack for partially…

Data Analysis, Statistics and Probability · Physics 2015-05-30 Gao-Gao Dong , Jian-Xi Gao , Li-Xin Tian , Rui-Jin Du , Ying-Huan He

Most current studies estimate the invulnerability of complex networks using a qualitative method that analyzes the inaccurate decay rate of network efficiency. This method results in confusion over the invulnerability of various types of…

Social and Information Networks · Computer Science 2014-02-18 Jun Qin , Hongrun Wu , Xiaonian Tong , Bojin Zheng

We study cascading failures in networks using a dynamical flow model based on simple conservation and distribution laws to investigate the impact of transient dynamics caused by the rebalancing of loads after an initial network failure…

Physics and Society · Physics 2010-05-04 Ingve Simonsen , Lubos Buzna , Karsten Peters , Stefan Bornholdt , Dirk Helbing
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