Related papers: Weak Multiplex Percolation
Classical blockmodel is known as the simplest among models of networks with community structure. The model can be also seen as an extremely simply example of interconnected networks. For this reason, it is surprising that the percolation…
Modular networks, such as critical infrastructures, are often built from distinct, densely connected modules (e.g., cities) that are sparsely interconnected. When such networks are gradually and randomly disrupted under a percolation…
Multiplex networks describe systems whose interactions can be of different nature, and are fundamental to understand complexity of networks beyond the framework of simple graphs. Recently it has been pointed out that restricting the…
Percolation refers to the emergence of a giant connected cluster in a disordered system when the number of connections between nodes exceeds a critical value. The percolation phase transitions were believed to be continuous until recently…
Drawing inspiration from real world interacting systems we study a system consisting of two networks that exhibit antagonistic and dependent interactions. By antagonistic and dependent interactions, we mean, that a proportion of functional…
We reconsider the problem of percolation on an equilibrium random network with degree-degree correlations between nearest-neighboring vertices focusing on critical singularities at a percolation threshold. We obtain criteria for…
We study a problem of failure of two interdependent networks in the case of correlated degrees of mutually dependent nodes. We assume that both networks (A and B) have the same number of nodes $N$ connected by the bidirectional dependency…
Almost all network research has been focused on the properties of a single network that does not interact and depends on other networks. In reality, many real-world networks interact with other networks. Here we develop an analytical…
This work presents exact expressions for size distributions of weak/multilayer connected components in two generalisations of the configuration model: networks with directed edges and multiplex networks with arbitrary number of layers. The…
Many complex systems can be described as multiplex networks in which the same nodes can interact with one another in different layers, thus forming a set of interacting and co-evolving networks. Examples of such multiplex systems are social…
A typical complex system should be described by a supernetwork or a network of networks, in which the networks are coupled to some other networks. As the first step to understanding the complex systems on such more systematic level,…
Correlations are known to play a crucial role in determining the structure of complex networks. Here we study how their presence affects the computation of the percolation threshold in random hypergraphs. In order to mimic the correlation…
Wireless multi-hop ad hoc communication networks represent an infrastructure-less and self-organized generalization of todays wireless cellular networks. Connectivity within such a network is an important issue. Continuum percolation and…
We present an exact mathematical framework able to describe site-percolation transitions in real multiplex networks. Specifically, we consider the average percolation diagram valid over an infinite number of random configurations where…
Percolation on networks is a common framework to model a wide range of processes, from cascading failures to epidemic spreading. Standard percolation assumes short-range interactions, implying that nodes can merge into clusters only if they…
The stochastic addition of either vertices or connections in a network leads to the observation of the percolation transition, a structural change with the appearance of a connected component encompassing a finite fraction of the system.…
Percolation theory can be used to describe the structural properties of complex networks using the generating function formulation. This mapping assumes that the network is locally tree-like and does not contain short-range loops between…
Many real-world complex systems are best modeled by multiplex networks. The multiplexity has proved to have broad impact on the system's structure and function. Most theoretical studies on multiplex networks to date, however, have largely…
We compare phase transition and critical phenomena of bond percolation on Euclidean lattices, nonamenable graphs, and complex networks. On a Euclidean lattice, percolation shows a phase transition between the nonpercolating phase and…
Nodes in a complex networked system often engage in more than one type of interactions among them; they form a multiplex network with multiple types of links. In real-world complex systems, a node's degree for one type of links and that for…