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We present a subjective selection of methods for complex systems analysis ranging from statistical tools through numerical methods based on AI to both linear and non-linear ODEs and PDEs. All the notions apply the network structure and are…

The new concept of multilevel network is introduced in order to embody some topological properties of complex systems with structures in the mesoscale which are not completely captured by the classical models. This new model, which…

Network percolation has recently been proposed as a method to characterize the global structure of an urban system form the bottom-up. This paper proposes to extend urban network percolation in a multi-dimensional way, to take into account…

Physics and Society · Physics 2019-03-19 Juste Raimbault

We introduce a minimal extended evolving model for small-world networks which is controlled by a parameter. In this model the network growth is determined by the attachment of new nodes to already existing nodes that are geographically…

Statistical Mechanics · Physics 2007-05-23 Zhongzhi Zhang , Lili Rong , Francesc Comellas

Benchmark scenarios are widely used in transportation research to evaluate routing algorithms, simulate infrastructure interventions, and test new technologies under controlled conditions. However, the structural and behavioral fidelity of…

Computational Engineering, Finance, and Science · Computer Science 2025-08-11 Chen Zhang , Timothy LaRock , Alben Rome Bagabaldo , Jürgen Hackl

The small-world networks recently introduced by Watts and Strogatz [Nature 393, 440 (1998)] has attracted much interests in studying the interesting properties of the networks without time-delay. However, a signal or influence travelling on…

Disordered Systems and Neural Networks · Physics 2010-03-26 Xin-She Yang

We analyze the public transport networks (PTNs) of a number of major cities of the world. While the primary network topology is defined by a set of routes each servicing an ordered series of given stations, a number of different…

Physics and Society · Physics 2009-11-13 Christian von Ferber , Taras Holovatch , Yurij Holovatch , Vasyl Palchykov

Small-world networks by Watts and Strogatz are a class of networks that are highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs. These characteristics result in networks with unique…

Adaptation and Self-Organizing Systems · Physics 2011-09-27 Qawi K. Telesford , Karen E. Joyce , Satoru Hayasaka , Jonathan H. Burdette , Paul J. Laurienti

Real-world networks exhibit prominent hierarchical and modular structures, with various subgraphs as building blocks. Most existing studies simply consider distinct subgraphs as motifs and use only their numbers to characterize the…

Social and Information Networks · Computer Science 2019-12-17 Qi Xuan , Jinhuan Wang , Minghao Zhao , Junkun Yuan , Chenbo Fu , Zhongyuan Ruan , Guanrong Chen

We review measures of street network structure proposed in the recent literature, establish their relevance to practice, and identify open challenges facing researchers. These measures' empirical values vary substantially across world…

Physics and Society · Physics 2024-09-13 Marc Barthelemy , Geoff Boeing

A main goal in the analysis of a complex system is to infer its underlying network structure from time-series observations of its behaviour. The inference process is often done by using bi-variate similarity measures, such as the…

Disordered Systems and Neural Networks · Physics 2019-09-06 Rodrigo A. García , Arturo C. Martí , Cecilia Cabeza , Nicolás Rubido

Complex systems are fascinating because their rich macroscopic properties emerge from the interaction of many simple parts. Understanding the building principles of these emergent phenomena in nature requires assessing natural complex…

Neurons and Cognition · Quantitative Biology 2022-11-17 Anna Levina , Viola Priesemann , Johannes Zierenberg

How to enhance the communication efficiency and quality on vehicular networks is one critical important issue. While with the larger and larger scale of vehicular networks in dense cities, the real-world datasets show that the vehicular…

Networking and Internet Architecture · Computer Science 2020-08-05 Jingjing Wang , Chunxiao Jiang , Longxiang Gao , Shui Yu , Zhu Han , Yong Ren

The small-world phenomenon is found in many self-organising systems. Systems configured in small-world networks spread information more easily than in random or regular lattice-type networks. Whilst it is a known fact that small-world…

Physics and Society · Physics 2015-08-17 Eugene Ch'ng

The human brain has been studied at multiple scales, from neurons, circuits, areas with well defined anatomical and functional boundaries, to large-scale functional networks which mediate coherent cognition. In a recent work, we addressed…

Biological Physics · Physics 2012-05-17 Lazaros K. Gallos , Mariano Sigman , Hernan A. Makse

Optimizing paths on networks is crucial for many applications, from subway traffic to Internet communication. As global path optimization that takes account of all path-choices simultaneously is computationally hard, most existing routing…

Physics and Society · Physics 2013-09-05 Chi Ho Yeung , David Saad , K. Y. Michael Wong

Complex networks representing social interactions, brain activities, molecular structures have been studied widely to be able to understand and predict their characteristics as graphs. Models and algorithms for these networks are used in…

Social and Information Networks · Computer Science 2022-10-24 Murat Çelik , Ali Baran Taşdemir , Lale Özkahya

In order to deal efficiently with the exponential growth of the Web services landscape in composition life cycle activities, it is necessary to have a clear view of its main features. As for many situations where there is a lot of…

Software Engineering · Computer Science 2013-05-03 Chantal Cherifi , Jean-François Santucci

Each complex network (or class of networks) presents specific topological features which characterize its connectivity and highly influence the dynamics of processes executed on the network. The analysis, discrimination, and synthesis of…

Disordered Systems and Neural Networks · Physics 2009-09-29 Luciano da F. Costa , Francisco A. Rodrigues , Gonzalo Travieso , P. R. Villas Boas

We study the distribution function for minimal paths in small-world networks. Using properties of this distribution function, we derive analytic results which greatly simplify the numerical calculation of the average minimal distance,…

Statistical Mechanics · Physics 2009-10-31 R. V. Kulkarni , E. Almaas , D. Stroud