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Topological landscape is introduced for networks with functions defined on the nodes. By extending the notion of gradient flows to the network setting, critical nodes of different indices are defined. This leads to a concise and…

Methodology · Statistics 2012-05-01 E. Weinan , Jianfeng Lu , Yuan Yao

To comprehend the hierarchical organization of large integrated systems, we introduce the hierarchical map equation, which reveals multilevel structures in networks. In this information-theoretic approach, we exploit the duality between…

Physics and Society · Physics 2011-04-12 M. Rosvall , C. T. Bergstrom

We introduce a heterogeneous connection model for network formation to capture the effect of cost heterogeneity on the structure of efficient networks. In the proposed model, connection costs are assumed to be separable, which means the…

Economics · Quantitative Finance 2015-12-14 Babak Heydari , Mohsen Mosleh , Kia Dalili

The paper investigates the properties of a class of resource allocation algorithms for communication networks: if a node of this network has $x$ requests to transmit, then it receives a fraction of the capacity proportional to $\log(1+x)$,…

Probability · Mathematics 2015-09-10 Philippe Robert , Amandine Véber

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

In this paper we consider spatial networks that realize a balance between an infrastructure cost (the cost of wire needed to connect the network in space) and communication efficiency, measured by average shortest pathlength. A global…

Disordered Systems and Neural Networks · Physics 2015-05-19 Markus Brede

The structure of communication networks is an important determinant of the capacity of teams, organizations and societies to solve policy, business and science problems. Yet, previous studies reached contradictory results about the…

Social and Information Networks · Computer Science 2016-10-24 Daniel Barkoczi , Mirta Galesic

Communication of signals among nodes in a complex network poses fundamental problems of efficiency and cost. Routing of messages along shortest paths requires global information about the topology, while spreading by diffusion, which…

Neurons and Cognition · Quantitative Biology 2019-06-19 Andrea Avena-Koenigsberger , Xiaoran Yan , Artemy Kolchinsky , Martijn van den Heuvel , Patric Hagmann , Olaf Sporns

Transport networks are crucial to the functioning of natural and technological systems. Nature features transport networks that are adaptive over a vast range of parameters, thus providing an impressive level of robustness in supply.…

Adaptation and Self-Organizing Systems · Physics 2017-11-28 Erik Andreas Martens , Konstantin Klemm

Understanding the mechanisms of neural communication in large-scale brain networks remains a major goal in neuroscience. We investigated whether navigation is a parsimonious routing model for connectomics. Navigating a network involves…

Neurons and Cognition · Quantitative Biology 2018-06-05 Caio Seguin , Martijn P. van den Heuvel , Andrew Zalesky

Reliable propagation of information through large networks, e.g., communication networks, social networks or sensor networks is very important in many applications concerning marketing, social networks, and wireless sensor networks.…

Data Structures and Algorithms · Computer Science 2018-05-08 Christian Frey , Andreas Züfle , Tobias Emrich , Matthias Renz

Driven by growing interest in the sciences, industry, and among the broader public, a large number of empirical studies have been conducted in recent years of the structure of networks ranging from the internet and the world wide web to…

Social and Information Networks · Computer Science 2018-06-08 M. E. J. Newman

Comparing weighted networks in neuroscience is hard, because the topological properties of a given network are necessarily dependent on the number of edges of that network. This problem arises in the analysis of both weighted and unweighted…

Applications · Statistics 2014-03-28 Cedric E. Ginestet , Arnaud P. Fournel , Andrew Simmons

For most technical networks, the interplay of dynamics, traffic and topology is assumed crucial to their evolution. In this paper, we propose a traffic-driven evolution model of weighted technological networks. By introducing a general…

Disordered Systems and Neural Networks · Physics 2009-11-11 Wen-Xu Wang , Bo Hu , Gang Yan , Qing Ou , Bing-Hong Wang

We report the results of an in-depth study of the role of graph topology on quantum transport efficiency in random removal and Watts-Strogatz networks. By using four different environmental models -- noiseless, driving by classical random…

Quantum Physics · Physics 2023-03-17 Arzu Kurt , Matteo A. C. Rossi , Jyrki Piilo

Recommendation systems represent an important tool for news distribution on the Internet. In this work we modify a recently proposed social recommendation model in order to deal with no explicit ratings of users on news. The model consists…

Physics and Society · Physics 2015-05-27 Dong Wei , Tao Zhou , Giulio Cimini , Pei Wu , Weiping Liu , Yi-Cheng Zhang

With the tremendous increase of the Internet traffic, achieving the best performance with limited resources is becoming an extremely urgent problem. In order to address this concern, in this paper, we build an optimization problem which…

Physics and Society · Physics 2017-02-23 Li Rui , Xia Yongxiang , Tse K Chi

It has been discovered recently that many social, biological and ecological systems have the so-called small-world and scale-free features, which has provoked new research interest in the studies of various complex networks. Yet, most…

Disordered Systems and Neural Networks · Physics 2007-05-23 Chunguang Li , Guanrong Chen

Resilient intermodal freight networks are vital for sustaining supply chains amid increasing threats from natural hazards and cyberattacks. While transportation resilience has been widely studied, understanding how random and targeted…

Physics and Society · Physics 2026-01-06 Aliza Sharmin , Bharat Sharma , Mustafa Can Camur , Olufemi A. Omitaomu , Xueping Li

We analyze transport on a graph with multiple constraints and where the weight of the edges connecting the nodes is a dynamical variable. The network dynamics results from the interplay between a nonlinear function of the flow, dissipation,…

Statistical Mechanics · Physics 2023-11-28 Frederic Folz , Kurt Mehlhorn , Giovanna Morigi