相关论文: Giant components in directed multiplex networks

We describe how to calculate the sizes of all giant connected components of a directed graph, including the {\em strongly} connected one. Just to the class of directed networks, in particular, belongs the World Wide Web. The results are…

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…

We reveal a hierarchical, multilayer organization of finite components -- i.e., tendrils and tubes -- around the giant connected components in directed networks and propose efficient algorithms allowing one to uncover the entire…

We describe the emergence of the giant mutually connected component in networks of networks in which each node has a single replica node in any layer and can be interdependent only on its replica nodes in the interdependent layers. We prove…

Complex networks are made up of vertices and edges. The edges, which may be directed or undirected, are equipped with positive weights. Modeling complex systems that consist of different types of objects leads to multilayer networks, in…

We study directed random graphs (random graphs whose edges are directed), and present new results on the so-called strong components of those graphs. We provide analytic and simulation results on two special classes of strong component,…

A common definition of a robust connection between two nodes in a network such as a communication network is that there should be at least two independent paths connecting them, so that the failure of no single node in the network causes…

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…

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…

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…

In many real, directed networks, the strongly connected component of nodes which are mutually reachable is very small. This does not fit with current theory, based on random graphs, according to which strong connectivity depends on mean…

We study a dynamical random network model in which at every construction step a new vertex is introduced and attached to every existing vertex independently with a probability proportional to a concave function f of its current degree. We…

A network is a typical expressive form of representing complex systems in terms of vertices and links, in which the pattern of interactions amongst components of the network is intricate. The network can be static that does not change over…

A complex system can be represented and analyzed as a network, where nodes represent the units of the network and edges represent connections between those units. For example, a brain network represents neurons as nodes and axons between…

Real networks often form interacting parts of larger and more complex systems. Examples can be found in different domains, ranging from the Internet to structural and functional brain networks. Here, we show that these multiplex systems are…

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…

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…

Complex networks are made up of vertices and edges. The latter connect the vertices. There are several ways to measure the importance of the vertices, e.g., by counting the number of edges that start or end at each vertex, or by using the…

From transportation networks to complex infrastructures, and to social and economic networks, a large variety of systems can be described in terms of multiplex networks formed by a set of nodes interacting through different network layers.…

We study the problem of the existence of a giant component in a random multipartite graph. We consider a random multipartite graph with $p$ parts generated according to a given degree sequence $n_i^{\mathbf{d}}(n)$ which denotes the number…