Related papers: Structural Inference of Hierarchies in Networks
Networks have in recent years emerged as an invaluable tool for describing and quantifying complex systems in many branches of science. Recent studies suggest that networks often exhibit hierarchical organization, where vertices divide into…
Many real networks in nature and society share two generic properties: they are scale-free and they display a high degree of clustering. We show that these two features are the consequence of a hierarchical organization, implying that small…
Hierarchy is one of the most conspicuous features of numerous natural, technological and social systems. The underlying structures are typically complex and their most relevant organizational principle is the ordering of the ties among the…
In recent years, the theory and application of complex networks have been quickly developing in a markable way due to the increasing amount of data from real systems and to the fruitful application of powerful methods used in statistical…
Our recent paper [Grauwin et al. Sci. Rep. 7 (2017)] demonstrates that community and hierarchical structure of the networks of human interactions largely determines the least and should be taken into account while modeling them. In the…
Modular and hierarchical community structures are pervasive in real-world complex systems. A great deal of effort has gone into trying to detect and study these structures. Important theoretical advances in the detection of modular have…
Hierarchical networks actually have many applications in the real world. Firstly, we propose a new class of hierarchical networks with scale-free and fractal structure, which are the networks with triangles compared to traditional…
We suggest an approach to study hierarchy, especially hidden one, of complex networks based on the analysis of their vulnerability. Two quantities are proposed as a measure of network hierarchy. The first one is the system vulnerability V.…
Network models with latent geometry have been used successfully in many applications in network science and other disciplines, yet it is usually impossible to tell if a given real network is geometric, meaning if it is a typical element in…
Hierarchy seems to pervade complexity in both living and artificial systems. Despite its relevance, no general theory that captures all features of hierarchy and its origins has been proposed yet. Here we present a formal approach resulting…
Graph vertices are often organized into groups that seem to live fairly independently of the rest of the graph, with which they share but a few edges, whereas the relationships between group members are stronger, as shown by the large…
Network motifs are characteristic patterns which occur in the networks essentially more frequently than the other patterns. For five motifs found in S. Itzkovitz, U. Alon, Phys. Rev.~E, 2005, 71, 026117-1, hierarchical random graphs are…
In this paper, we consider the problem of exploring structural regularities of networks by dividing the nodes of a network into groups such that the members of each group have similar patterns of connections to other groups. Specifically,…
Formation of a hierarchy within an organization is a natural way of assigning the duties, delegating responsibilities and optimizing the flow of information. Only for the smallest companies the lack of the hierarchy, that is, a flat one, is…
We introduce a class of random graphs with a community structure, which we call the hierarchical configuration model. On the inter-community level, the graph is a configuration model, and on the intra-community level, every vertex in the…
A number of recent studies have focused on the statistical properties of networked systems such as social networks and the World-Wide Web. Researchers have concentrated particularly on a few properties which seem to be common to many…
Latent variable models for network data extract a summary of the relational structure underlying an observed network. The simplest possible models subdivide nodes of the network into clusters; the probability of a link between any two nodes…
Common experience suggests that many networks might possess community structure - division of vertices into groups, with a higher density of edges within groups than between them. Here we describe a new computer algorithm that detects…
Most complex systems can be captured by graphs or networks. Networks connect nodes (e.g.\ neurons) through edges (synapses), thus summarizing the system's structure. A popular way of interrogating graphs is community detection, which…
The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of…