Nature Physics Insight – Complexity

In many large ensembles, the property of the system as a whole cannot be understood from studying the individual entities alone — these ensembles can be made up by neurons in the brain, transport users in traffic networks or data packages in the Internet. The past decade has seen important progress in our fundamental understanding of what such seemingly disparate 'complex systems' have in common; some of these advances are surveyed here.



Complexity - p13

Andreas Trabesinger




The network takeover - pp14 – 16

Albert-László Barabási


Reductionism, as a paradigm, is expired, and complexity, as a field, is tired. Data-based mathematical models of complex systems are offering a fresh perspective, rapidly developing into a new discipline: network science.



Between order and chaos pp17 – 24

James Crutchfield


A completely ordered universe is as unexciting as an entirely disordered one. Interesting 'complex' phenomena arise in a middle ground. This article reviews the tools that have been developed to quantify structural complexity and to automatically discover patterns hidden between order and chaos.

Communities, modules and large-scale structure in networks pp25 – 31

M. E. J. Newman


Networks have proved to be useful representations of complex systems. Within these networks, there are typically a number of subsystems defined by only a subset of nodes and edges. Detecting these structures often provides important information about the organization and functioning of the overall network. Here, progress towards quantifying medium- and large-scale structures within complex networks is reviewed.

Modelling dynamical processes in complex socio-technical systems pp32 – 39

Alessandro Vespignani


Vast amounts of data are available about complex technological systems and how we use them. These data provide the basis not only for mapping out connectivity patterns, but also for the study of dynamical phenomena, including epidemic outbreaks and routing of information through computer networks. This article reviews the fundamental tools for modelling such dynamical processes and discusses a number of applications.


Progress Article

Networks formed from interdependent networks pp40 – 48

Jianxi Gao, Sergey V. Buldyrev, H. Eugene Stanley and Shlomo Havlin


Aspects concerning the structure and behaviours of individual networks have been studied intensely in the past decade, but the exploration of interdependent systems in the context of complex networks has started only recently. This article reviews a general framework for modelling the percolation properties of interacting networks and the first results drawn from its study.


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