Related papers: Giant components in directed multiplex networks
The recursive removal of leaves (dead end vertices) and their neighbors from an undirected network results, when this pruning algorithm stops, in a so-called core of the network. This specific subgraph should be distinguished from…
Two different types of directed networks are investigated, transcriptional regulation networks and neural networks. The directed network structure are studied and also shown to reflect the different processes taking place on the networks.…
Directed acyclic graphs are a fundamental class of networks that includes citation networks, food webs, and family trees, among others. Here we define a random graph model for directed acyclic graphs and give solutions for a number of the…
Various different random graph models have been proposed in which the vertices of the graph are seen as members of a metric space, and edges between vertices are determined as a function of the distance between the corresponding metric…
A number of network structural characteristics have recently been the subject of particularly intense research, including degree distributions, community structure, and various measures of vertex centrality, to mention only a few. Vertices…
Data describing the three-dimensional structure of physical networks is increasingly available, leading to a surge of interest in network science to explore the relationship between the shape and connectivity of physical networks. We…
Networks constitute efficient tools for assessing universal features of complex systems. In physical contexts, classical as well as quantum, networks are used to describe a wide range of phenomena, such as phase transitions, intricate…
The micro-structure of the giant component of the Erd{\H o}s-R\'enyi network and other configuration model networks is analyzed using generating function methods. While configuration model networks are uncorrelated, the giant component…
We analyze the stability of the network's giant connected component under impact of adverse events, which we model through the link percolation. Specifically, we quantify the extent to which the largest connected component of a network…
We study connected graphs with a fixed degree sequence, in the sparse setting where the number of edges grows linearly in the number of vertices. Using the relation to the configuration model, we identify the number of such connected graphs…
We study the emergence of a giant component in the configuration model subject to additional constraints on the edges. We partition a $d$-dimensional torus into a cubic lattice with a diverging number of compartments containing vertices and…
In the infinite configuration network the links between nodes are assigned randomly with the only restriction that the degree distribution has to match a predefined function. This work presents a simple equation that gives for an arbitrary…
A directed graph G (V, E) is strongly connected if and only if, for a pair of vertices X and Y from V, there exists a path from X to Y and a path from Y to X. In Computer Science, the partition of a graph in strongly connected components is…
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…
Real world complex networks often exhibit multiplex structure, connecting entities from different aspects of physical systems such as social, transportation and biological networks. Little is known about general properties of such networks…
Modularity is one of the most prominent properties of real-world complex networks. Here, we address the issue of module identification in two important classes of networks: bipartite networks and directed unipartite networks. Nodes in…
Many real complex systems cannot be represented by a single network, but due to multiple sub-systems and types of interactions, must be represented as a multiplex network. This is a set of nodes which exist in several layers, with each…
The structure of complex networks has been of interest in many scientific and engineering disciplines over the decades. A number of studies in the field have been focused on finding the common properties among different kinds of networks…
We study the joint components in a random `double graph' that is obtained by superposing red and blue binomial random graphs on $n$~vertices. A joint component is a maximal set of vertices, which contains both a red and a blue spanning…
Stochastic Kronecker graphs are a model for complex networks where each edge is present independently according the Kronecker (tensor) product of a fixed matrix k-by-k matrix P with entries in [0,1]. We develop a novel correspondence…