Related papers: Directed network modules
The notion of k-clique percolation in random graphs is introduced, where k is the size of the complete subgraphs whose large scale organizations are analytically and numerically investigated. For the Erdos-Renyi graph of N vertices we…
The widespread relevance of increasingly complex networks requires methods to extract meaningful coarse-grained representations of such systems. For undirected graphs, standard community detection methods use criteria largely based on…
We consider the problem of finding communities or modules in directed networks. The most common approach to this problem in the previous literature has been simply to ignore edge direction and apply methods developed for community discovery…
Directed networks are ubiquitous and are necessary to represent complex systems with asymmetric interactions---from food webs to the World Wide Web. Despite the importance of edge direction for detecting local and community structure, it…
The random graph of Erdos and Renyi is one of the oldest and best studied models of a network, and possesses the considerable advantage of being exactly solvable for many of its average properties. However, as a model of real-world networks…
Methods for determining the percolation threshold usually study the behavior of network ensembles and are often restricted to a particular type of probabilistic node/link removal strategy. We propose a network-specific method to determine…
Most networks found in social and biochemical systems have modular structures. An important question prompted by the modularity of these networks is whether nodes can be said to belong to a single group. If they cannot, we would need to…
To better understand the overlapping modular organization of large networks with respect to flow, here we introduce the map equation for overlapping modules. In this information-theoretic framework, we use the correspondence between…
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…
Modern network analysis often involves multi-layer network data in which the nodes are aligned, and the edges on each layer represent one of the multiple relations among the nodes. Current literature on multi-layer network data is mostly…
Bipartite networks provide an effective resource for representing, characterizing, and modeling several abstract and real-world systems and structures involving binary relations, which include food webs, social interactions, and…
We develop a new ensemble of modular random graphs in which degree-degree correlations can be different in each module and the inter-module connections are defined by the joint degree-degree distribution of nodes for each pair of modules.…
Many real-world networks are intrinsically directed. Such networks include activation of genes, hyperlinks on the internet, and the network of followers on Twitter among many others. The challenge, however, is to create a network model that…
Many real-world complex systems are characterized by non-pairwise -- higher-order -- interactions among system's units, and can be effectively modeled as hypergraphs. Directed hypergraphs distinguish between source and target sets within…
Network embedding is a fervid topic in current networks science and observes that most real complex systems can be embedded in hidden metrics space and emerge as the geometrical property, where the geometric distance between nodes…
Identifying the nodes that must be directly controlled to steer a network along a desired trajectory remains an open problem for digraphs, and even more so for hypergraphs. In this manuscript, we investigate network systems coupled via…
We define an approach to identify overlapping communities in multiplex networks, extending the popular clique percolation method for simple graphs. The extension requires to rethink the basic concepts on which the clique percolation…
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…
Rich-club and page-club coefficients and their null models are introduced for directed graphs. Null models allow for a quantitative discussion of the rich-club and page-club phenomena. These coefficients are computed for four directed…
Directed networks such as gene regulation networks and neural networks are connected by arcs (directed links). The nodes in a directed network are often strongly interwound by a huge number of directed cycles, which lead to complex…