Related papers: Strong Connectivity in Real Directed Networks
Percolation, the formation of a macroscopic connected component, is a key feature in the description of complex networks. The dynamical properties of a variety of systems can be understood in terms of percolation, including the robustness…
Modeling how networks change under structural perturbations can yield foundational insights into network robustness, which is critical in many real-world applications. The largest connected component is a popular measure of network…
The function of a real network depends not only on the reliability of its own components, but is affected also by the simultaneous operation of other real networks coupled with it. Robustness of systems composed of interdependent network…
An important class of real-world networks have directed edges, and in addition, some rank ordering on the nodes, for instance the "popularity" of users in online social networks. Yet, nearly all research related to explosive percolation has…
Many networks describing complex systems are directed: the interactions between elements are not symmetric. Recent work has shown that these networks can display properties such as trophic coherence or non-normality, which in turn affect…
The traditional node percolation map of directed networks is reanalyzed in terms of edges. In the percolated phase, edges can mainly organize into five distinct giant connected components, interfaces bridging the communication of nodes in…
We introduce a model for dynamic networks, where the links or the strengths of the links change over time. We solve the model by mapping dynamic networks to the problem of directed percolation, where the direction corresponds to the…
Knowing which nodes are influential in a complex network and whether the network can be influenced by a small subset of nodes is a key part of network analysis. However, many traditional measures of importance focus on node level…
The event graph representation of temporal networks suggests that the connectivity of temporal structures can be mapped to a directed percolation problem. However, similar to percolation theory on static networks, this mapping is valid…
The lack of studying the complex organization of directed network usually limits to the understanding of underlying relationship between network structures and functions. Structural controllability and structural predictability, two…
Communication networks, power grids, and transportation networks are all examples of networks whose performance depends on reliable connectivity of their underlying network components even in the presence of usual network dynamics due to…
We consider a class of random, weighted networks, obtained through a redefinition of patterns in an Hopfield-like model and, by performing percolation processes, we get information about topology and resilience properties of the networks…
In many systems consisting of interacting subsystems, the complex interactions between elements can be represented using multilayer networks. However percolation, key to understanding connectivity and robustness, is not trivially…
Recent work on the internet, social networks, and the power grid has addressed the resilience of these networks to either random or targeted deletion of network nodes. Such deletions include, for example, the failure of internet routers or…
As a fundamental structural transition in complex networks, core percolation is related to a wide range of important problems. Yet, previous theoretical studies of core percolation have been focusing on the classical Erd\H{o}s-R\'enyi…
We explore the relation between the topological relevance of a node in a complex network and the individual dynamics it exhibits. When the system is weakly coupled, the effect of the coupling strength against the dynamical complexity of the…
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…
Directed networks are essential for representing complex systems, capturing the asymmetry of interactions in fields such as neuroscience, transportation, and social networks. Directionality reveals how influence, information, or resources…
Percolation theory is extensively studied in statistical physics and mathematics with applications in diverse fields. However, the research is focused on systems with only one type of links, connectivity links. We review a recently…
Analytical approaches to model the structure of complex networks can be distinguished into two groups according to whether they consider an intensive (e.g., fixed degree sequence and random otherwise) or an extensive (e.g., adjacency…