Multilayer Networks in a Nutshell

Complex systems are characterized by many interacting units that give rise to emergent behavior. A particularly advantageous way to study these systems is through the analysis of the networks that encode the interactions among the system's constituents. During the last two decades, network science has provided many insights in natural, social, biological and technological systems. However, real systems are more often than not interconnected, with many interdependencies that are not properly captured by single layer networks. To account for this source of complexity, a more general framework, in which different networks evolve or interact with each other, is needed. These are known as multilayer networks. Here we provide an overview of the basic methodology used to describe multilayer systems as well as of some representative dynamical processes that take place on top of them. We round off the review with a summary of several applications in diverse fields of science.Comment: 16 pages and 3 figures. Submitted for publicatio

Weak nodes detection in urban transport systems: Planning for resilience in Singapore

The availability of massive data-sets describing human mobility offers the possibility to design simulation tools to monitor and improve the resilience of transport systems in response to traumatic events such as natural and man-made disasters (e.g. floods terroristic attacks, etc...). In this perspective, we propose ACHILLES, an application to model people's movements in a given transport system mode through a multiplex network representation based on mobility data. ACHILLES is a web-based application which provides an easy-to-use interface to explore the mobility fluxes and the connectivity of every urban zone in a city, as well as to visualize changes in the transport system resulting from the addition or removal of transport modes, urban zones, and single stops. Notably, our application allows the user to assess the overall resilience of the transport network by identifying its weakest node, i.e. Urban Achilles Heel, with reference to the ancient Greek mythology. To demonstrate the impact of ACHILLES for humanitarian aid we consider its application to a real-world scenario by exploring human mobility in Singapore in response to flood prevention.Comment: 9 pages, 6 figures, IEEE Data Science and Advanced Analytic

Modeling the Multi-layer Nature of the European Air Transport Network: Resilience and Passengers Re-scheduling under random failures

We study the dynamics of the European Air Transport Network by using a multiplex network formalism. We will consider the set of flights of each airline as an interdependent network and we analyze the resilience of the system against random flight failures in the passenger's rescheduling problem. A comparison between the single-plex approach and the corresponding multiplex one is presented illustrating that the multiplexity strongly affects the robustness of the European Air Network.Comment: 12 pages, 5 figures - Accepted for publication in European Physical Journal Special Topic

Towards real-world complexity: an introduction to multiplex networks

Many real-world complex systems are best modeled by multiplex networks of interacting network layers. The multiplex network study is one of the newest and hottest themes in the statistical physics of complex networks. Pioneering studies have proven that the multiplexity has broad impact on the system's structure and function. In this Colloquium paper, we present an organized review of the growing body of current literature on multiplex networks by categorizing existing studies broadly according to the type of layer coupling in the problem. Major recent advances in the field are surveyed and some outstanding open challenges and future perspectives will be proposed.Comment: 20 pages, 10 figure