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Percolation establishes the connectivity of complex networks and is one of the most fundamental critical phenomena for the study of complex systems. On simple networks, percolation displays a second-order phase transition; on multiplex…
Percolation in complex networks is viewed as both: a process that mimics network degradation and a tool that reveals peculiarities of the underlying network structure. During the course of percolation, networks undergo non-trivial…
We analyse the flow of information in multiplex networks by means of the communicability function. First, we generalize this measure from its definition from simple graphs to multiplex networks. Then, we study its relevance for the analysis…
Real-world social and economic networks typically display a number of particular topological properties, such as a giant connected component, a broad degree distribution, the small-world property and the presence of communities of densely…
Modern communication networks are inherently complex in nature. First of all, they have a large number of heterogeneous components. Secondly, their connectivity is extremely dynamic. Nodes can come and go, links can be removed and added…
We use the concept of the network communicability (Phys. Rev. E 77 (2008) 036111) to define communities in a complex network. The communities are defined as the cliques of a communicability graph, which has the same set of nodes as the…
We introduce the notion of a network's conduciveness, a probabilistically interpretable measure of how the network's structure allows it to be conducive to roaming agents, in certain conditions, from one portion of the network to another.…
Percolation is a model for random damage to a network. It is one of the simplest models that displays a phase transition: when the network is severely damaged, it falls apart in many small connected components, while if the damage is light,…
Heat diffusion describes the process by which heat flows from areas with higher temperatures to ones with lower temperatures. This concept was previously adapted to graph structures, whereby heat flows between nodes of a graph depending on…
Graph theory constitutes a widely used and established field providing powerful tools for the characterization of complex networks. The intricate topology of networks can also be investigated by means of the collective dynamics observed in…
In this paper, we study the phase transition behavior emerging from the interactions among multiple agents in the presence of noise. We propose a simple discrete-time model in which a group of non-mobile agents form either a fixed connected…
Crystals arise as the result of the breaking of a spatial translation symmetry. Similarly, translation symmetries can also be broken in time so that discrete time crystals appear. Here, we introduce a method to describe, characterize, and…
Using the theory of diffusion in graphs, we propose a model to study mesoscopic transport through a diffusive quantum dot. The graph consists of three quasi-1D regions: a central region describing the dot, and two identical left- and right-…
Percolation transition is widely observed in networks ranging from biology to engineering. While much attention has been paid to network topologies, studies rarely focus on critical percolation phenomena driven by network dynamics. Using…
An exactly solvable model for the rewiring dynamics of weighted, directed networks is introduced. Simulations indicate that the model exhibits two types of condensation: (i) a phase in which, for each node, a finite fraction of its total…
Random graphs have played an instrumental role in modelling real-world networks arising from the internet topology, social networks, or even protein-interaction networks within cells. Percolation, on the other hand, has been the fundamental…
Complex network theory provides an elegant and powerful framework to statistically investigate different types of systems such as society, brain or the structure of local and long-range dynamical interrelationships in the climate system.…
In network science complex systems are represented as a mathematical graphs consisting of a set of nodes representing the components and a set of edges representing their interactions. The framework of networks has led to significant…
This work discusses the homogenization analysis for diffusion processes on scale-free metric graphs, using weak variational formulations. The oscillations of the diffusion coefficient along the edges of a metric graph induce internal…
Routing information through networks is a universal phenomenon in both natural and manmade complex systems. When each node has full knowledge of the global network connectivity, finding short communication paths is merely a matter of…