Complex networks articles within Nature Physics

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  • Article |

    Dense suspensions are granular materials suspended in a liquid at high packing fractions, exhibiting high viscosity. The latter is now shown to be related to the formation of a network of rigid clusters at large shear stress.

    • Michael van der Naald
    • , Abhinendra Singh
    •  & Heinrich M. Jaeger

  • Article |

    The strengths of connections in networks of neurons are heavy-tailed, with some neurons connected much more strongly than most. Now a simple network model can explain how this heavy-tailed connectivity emerges across four different species.

    • Christopher W. Lynn
    • , Caroline M. Holmes
    •  & Stephanie E. Palmer

  • Article |

    Topological features such as modularity and small-worldness are common in real-world networks. The emergence of such features may be driven by a trade-off between information exchange and response diversity that resembles thermodynamic efficiency.

    • Arsham Ghavasieh
    •  & Manlio De Domenico

  • News & Views |

    Predicting the large-scale behaviour of complex systems is challenging because of their underlying nonlinear dynamics. Theoretical evidence now verifies that many complex systems can be simplified and still provide an insightful description of the phenomena of interest.

    • Jianxi Gao

  • Article |

    Although using low-rank matrices is the go-to approach to model the dynamics of complex systems, its validity remains formally unconfirmed. An analysis of random networks and real-world data now sheds light on this low-rank hypothesis and its implications.

    • Vincent Thibeault
    • , Antoine Allard
    •  & Patrick Desrosiers

  • News & Views |

    Physical networks, composed of nodes and links that occupy a spatial volume, are hard to study with conventional techniques. A meta-graph approach that elucidates the impact of physicality on network structure has now been introduced.

    • Zoltán Toroczkai

  • Article |

    Physical networks are systems composed of physical entities, which conventional graph-based approaches fail to capture. Theoretical work now introduces a meta-graph technique to uncover the impact of physicality on the structure of networks.

    • Márton Pósfai
    • , Balázs Szegedy
    •  & Albert-László Barabási

  • Article |

    Network geometry is an emerging framework used to describe several topological and organizational features of complex networks. Now this approach has been extended to directed networks, which contain both symmetric and asymmetric interactions.

    • Antoine Allard
    • , M. Ángeles Serrano
    •  & Marián Boguñá

  • Review Article |

    Describing interdependencies and coupling between complex systems requires tools beyond what the framework of single networks offers. This Review covers recent developments in the study and modelling of multilayer networks.

    • Manlio De Domenico

  • News & Views |

    Research in the past few decades has uncovered powerful generalities in the structure of many natural and built networks. Now, a study describes how certain structural properties of networks may cause them to endure or collapse over time.

    • Neo D. Martinez
    •  & Richard J. Williams

  • Research Briefing |

    An experimental platform comprising two disordered superconductors separated by a thermally conducting electrical insulator represents a controllable physical system of interdependent networks. This system is modelled by thermally coupled networks of Josephson junctions. This platform could provide insights into theoretical multiscale phenomena, such as cascading tipping points or self-organized branching processes.

  • Article |

    Interdependent networks display many interesting properties, but have not been studied in laboratory experiments because of the lack of a platform that manifests appropriate couplings. Now, a network of disordered superconductors accomplishes this.

    • I. Bonamassa
    • , B. Gross
    •  & S. Havlin

  • Article |

    Despite looking highly irregular, most real-world networks exhibit natural stability to external perturbations. A study of the properties of the stability matrix of networks now sheds light on the principles underlying this emerging stability.

    • Chandrakala Meena
    • , Chittaranjan Hens
    •  & Baruch Barzel

  • News & Views |

    Renormalization is a technique based on a repeated coarse-graining procedure used to study scale invariance and criticality in statistical physics. Now, an expansion of the renormalization toolbox allows to explore scale invariance in real-world networks.

    • Konstantin Klemm

  • Article
    | Open Access

    The renormalization group method is routinely employed in studies of criticality in many areas of physics. A framework based on a field theoretical description of information diffusion now extends this tool to the study of complex networks.

    • Pablo Villegas
    • , Tommaso Gili
    •  & Andrea Gabrielli

  • Comment |

    A fundamental technical challenge in the analysis of network data is the automated discovery of communities — groups of nodes that are strongly connected or that share similar features or roles. In this Comment we review progress in the field over the past 20 years.

    • Santo Fortunato
    •  & Mark E. J. Newman

  • Article |

    Uncovering structures in temporal networks requires different tools than in their static counterparts. A metric now quantifies whether the nodes with a large number of connections also tend to stay simultaneously connected for longer times.

    • Nicola Pedreschi
    • , Demian Battaglia
    •  & Alain Barrat

  • News & Views |

    Predicting collapses of a complex system is notoriously hard. Finding ways to pull a collapsed system back to normal is even harder. A theoretical study now shows how reviving a single unit of a failed network might restore its whole functionality.

    • Patrick Desrosiers
    •  & Xavier Roy-Pomerleau

  • Article |

    Perturbations and disturbances can bring complex networks into undesirable states in which global functionality is suppressed. Now, a recovery scheme explains how to revive a damaged network by controlling only a small number of nodes.

    • Hillel Sanhedrai
    • , Jianxi Gao
    •  & Baruch Barzel

  • Article |

    Network models rarely fix the number of connections of each node during evolution, despite this being needed in real-world applications. Addressing this need, a new approach can grow scale-free networks without preferential attachment.

    • Shubha R. Kharel
    • , Tamás R. Mezei
    •  & Zoltan Toroczkai

  • Perspective |

    Network representations of complex systems are limited to pairwise interactions, but real-world systems often involve higher-order interactions. This Perspective looks at the new physics emerging from attempts to characterize these interactions.

    • Federico Battiston
    • , Enrico Amico
    •  & Giovanni Petri

  • Measure for Measure |

    What does it mean for an individual to be ‘important’ or for a connection to be ‘outstanding’? The answer depends on context, as Sarah Shugars and Samuel V. Scarpino explain.

    • Sarah Shugars
    •  & Samuel V. Scarpino

  • Article |

    Contact tracing is key to epidemic control, but network analysis now suggests that whom you infect may not be as pertinent a question as who infected you. Biases due to contact heterogeneity reveal the efficacy of backward over forward tracing.

    • Sadamori Kojaku
    • , Laurent Hébert-Dufresne
    •  & Yong-Yeol Ahn

  • Article |

    The ability to perform multiple tasks simultaneously is a key characteristic of parallel architectures. Using methods from statistical physics, this study provides analytical results that quantify the limitations of processing capacity for different types of tasks in neural networks.

    • Giovanni Petri
    • , Sebastian Musslick
    •  & Jonathan D. Cohen

  • Comment |

    The uncertainty associated with epidemic forecasts is often simulated with ensembles of epidemic trajectories based on combinations of parameters. We show that the standard approach for summarizing such ensembles systematically suppresses critical epidemiological information.

    • Jonas L. Juul
    • , Kaare Græsbøll
    •  & Sune Lehmann

  • Letter |

    Recently, a framework was introduced to model three-dimensional physical networks, such as brain or vascular ones, in a way that does not allow link crossings. Here the authors combine concepts from knot theory and statistical mechanics to be able to distinguish between physical networks with identical wiring but different layouts.

    • Yanchen Liu
    • , Nima Dehmamy
    •  & Albert-László Barabási

  • Article |

    The arrangement of a sequence of stimuli affects how humans perceive information. Here, the authors show experimentally that humans perceive information in a way that depends on the network structure of stimuli.

    • Christopher W. Lynn
    • , Lia Papadopoulos
    •  & Danielle S. Bassett

  • Article |

    The mathematical modelling of how information spreads in social networks has latterly gained fresh urgency. A study of realistic structured populations now identifies the threshold at which the propagation of rumours becomes contagious, thereby inducing a phase transition.

    • Jessica T. Davis
    • , Nicola Perra
    •  & Alessandro Vespignani

  • Letter |

    Knowledge of the spreading mechanisms of contagions is important for understanding a range of epidemiological and social problems. A study now shows that so-called simple and complex contagions cannot be told apart if there is more than one simple contagion traversing the population at the same time.

    • Laurent Hébert-Dufresne
    • , Samuel V. Scarpino
    •  & Jean-Gabriel Young

  • Article |

    Percolation transitions underpin a generic class of phenomena associated with the degree of connectedness in networks. A detailed numerical study now uncovers a universal scaling in the size of the largest cluster identified in such percolation models.

    • Jingfang Fan
    • , Jun Meng
    •  & Jan Nagler

  • Article |

    Mode-locking of lasers can be understood as self-organization, and the three-dimensional case of spatiotemporal mode-locking can described using attractor dissection theory, which helps develop an intuition for this complex case.

    • Logan G. Wright
    • , Pavel Sidorenko
    •  & Frank W. Wise

  • Article |

    An experiment with three alternating-current generators demonstrates converse symmetry breaking—a phenomenon whereby the system achieves frequency synchronization when its component systems are tuned asymmetrically.

    • Ferenc Molnar
    • , Takashi Nishikawa
    •  & Adilson E. Motter

  • Letter |

    The crease patterns for origami-based mechanical metamaterials can fold into myriad 3D shapes, but predicting foldability is no simple task. A framework for designing foldable patterns offers a neat alternative to extensive computer optimization.

    • Peter Dieleman
    • , Niek Vasmel
    •  & Martin van Hecke

  • Research Highlight |

    • Abigail Klopper

  • News & Views |

    The mechanics of many materials can be modelled by a network of balls connected by springs. A bottom-up approach based on differential geometry now captures changes in mechanics upon network growth or merger, going beyond the linear deformation regime.

    • A. Souslov
    •  & V. Vitelli

  • Perspective |

    Rich data are revealing that complex dependencies between the nodes of a network may not be captured by models based on pairwise interactions. Higher-order network models go beyond these limitations, offering new perspectives for understanding complex systems.

    • Renaud Lambiotte
    • , Martin Rosvall
    •  & Ingo Scholtes

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