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Recently increasing attention has been addressed to the fluctuations observed in percolation defined in single and multiplex networks. These fluctuations are extremely important to characterize the robustness of real finite networks but…
Multiplex networks are receiving increasing interests because they allow to model relationships between networked agents on several layers simultaneously. In this supplementary material for the paper "Navigability of interconnected networks…
In real networks complex topological features are often associated with a diversity of interactions as measured by the weights of the links. Moreover, spatial constraints may as well play an important role, resulting in a complex interplay…
In the context of epidemic spreading, many intricate dynamical patterns can emerge due to the cooperation of different types of pathogens or the interaction between the disease spread and other failure propagation mechanism. To unravel such…
The toughness of a polymer material can increase significantly if two networks are combined into one material. This toughening effect is a consequence of a transition from a brittle to a ductile failure response. Although this transition…
Adaptive networks are a versatile approach to model phenomena such as contagion and spreading dynamics, critical transitions and structure formation that emerge from the dynamic coevolution of complex network structure and node states.…
A crucial challenge in network theory is the study of the robustness of a network after facing a sequence of failures. In this work, we propose a dynamical definition of network's robustness based on Information Theory, that considers…
Multi-layered networks represent a major advance in the description of natural complex systems, and their study has shed light on new physical phenomena. Despite its importance, however, the role of the temporal dimension in their structure…
Graphs are pervasive in our everyday lives, with relevance to biology, the internet, and infrastructure, as well as numerous other applications. It is thus necessary to have an understanding as to how quickly a graph disintegrates, whether…
Multiplex networks (a system of multiple networks that have different types of links but share a common set of nodes) arise naturally in a wide spectrum of fields. Theoretical studies show that in such multiplex networks, correlated edge…
We propose a framework to understand the unprecedented performance and robustness of deep neural networks using field theory. Correlations between the weights within the same layer can be described by symmetries in that layer, and networks…
The power grid defines one of the most important technological networks of our times and sustains our complex society. It has evolved for more than a century into an extremely huge and seemingly robust and well understood system. But it…
Complex networks have been shown to be robust against random structural perturbations, but vulnerable against targeted attacks. Robustness analysis usually simulates the removal of individual or sets of nodes, followed by the assessment of…
Complex network theory aims to model and analyze complex systems that consist of multiple and interdependent components. Among all studies on complex networks, topological structure analysis is of the most fundamental importance, as it…
The characterization of various properties of real-world systems requires the knowledge of the underlying network of connections among the system's components. Unfortunately, in many situations the complete topology of this network is…
We introduce a model to study the delicate relation between the spreading of information and the formation of opinions in social systems. For this purpose, we propose a two-layer multiplex network model in which consensus dynamics takes…
We reveal large fluctuations in the response of real multiplex networks to random damage of nodes. These results indicate that the average response to random damage, traditionally considered in mean-field approaches to percolation, is a…
Complex networks, such as transportation networks, social networks, or biological networks, capture the complex system they model often by representing only one type of interactions. In real world systems, there may be many different…
Multilayer networks provide a framework to study complex systems with multiple types of interactions, multiple dynamical processes, and/or multiple subsystems. When studying a dynamical process on a multilayer network, it is important to…
In an increasingly connected world, the resilience of networked dynamical systems is important in the fields of ecology, economics, critical infrastructures, and organizational behaviour. Whilst we understand small-scale resilience well,…