Introduction to Focus Issue: Complex Dynamics in Networks, Multilayered Structures and Systems

In the last years, network scientists have directed their interest to the multi-layer character of real-world systems, and explicitly considered the structural and dynamical organization of graphs made of diverse layers between its constituents. Most complex systems include multiple subsystems and layers of connectivity and, in many cases, the interdependent components of systems interact through many different channels. Such a new perspective is indeed found to be the adequate representation for a wealth of features exhibited by networked systems in the real world. The contributions presented in this Focus Issue cover, from different points of view, the many achievements and still open questions in the field of multi-layer networks, such as: new frameworks and structures to represent and analyze heterogeneous complex systems, different aspects related to synchronization and centrality of complex networks, interplay between layers, and applications to logistic, biological, social, and technological fields.
Most of the real and engineered systems have multiple subsystems and layers of connectivity. In fact, there is a wide range of systems in the real world where components cannot function independently, and these components interact with others through different channels of connectivity and dependencies. Networked systems in fields as disparate as sociology (social networks, acquaintances, or collaborations between individuals), biology (metabolic and protein networks, neural networks), or technology (phone call networks, computers in telecommunication networks)1,3,7,14–16 may be described and analyzed by using a multi-layer representation.6,10 Fifteen years of new advances and approaches have been fruitfully exploited in technology, biology, and sociology, resulting in several extensions of complex networks to multi-structure or multi-relational networks, in order to combine the local scale with the global and the mesoscale structures of the system.