Related papers: Hierarchy depth in directed networks
Signs of hierarchy are prevalent in a wide range of systems in nature and society. One of the key problems is quantifying the importance of hierarchical organisation in the structure of the network representing the interactions or…
With the increasing availability of behavioral data from diverse digital sources, such as social media sites and cell phones, it is now possible to obtain detailed information about the structure, strength, and directionality of social…
The structure of a complex network plays a crucial role in determining its dynamical properties. In this work, we show that the the degree to which a network is directed and hierarchically organised is closely associated with the degree to…
Confining an answer to the question whether and how the coherent operation of network elements is determined by the the network structure is the topic of our work. We map the structure of signal flow in directed networks by analysing the…
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.…
Analyzing and characterizing the differences between networks is a fundamental and challenging problem in network science. Previously, most network comparison methods that rely on topological properties have been restricted to measuring…
A search technique locating network modules, i.e., internally densely connected groups of nodes in directed networks is introduced by extending the Clique Percolation Method originally proposed for undirected networks. After giving a…
The study of triangles in graphs is a standard tool in network analysis, leading to measures such as the \emph{transitivity}, i.e., the fraction of paths of length $2$ that participate in triangles. Real-world networks are often directed,…
Following the model introduced by Aguech, Lasmar and Mahmoud [Probab. Engrg. Inform. Sci. 21 (2007) 133-141], the weighted depth of a node in a labelled rooted tree is the sum of all labels on the path connecting the node to the root. We…
We define a new measure of network symmetry that is capable of capturing approximate global symmetries of networks. We apply this measure to different networks sampled from several classic network models, as well as several real-world…
Gurski and Wanke showed that a graph class C has bounded tree-width if and only if its associated class of directed line graphs has bounded clique-width. Inevitably -- asking whether this relationship lifts to directed graphs -- we…
Growing attention has been brought to the fact that many real directed networks exhibit hierarchy and directionality as measured through techniques like Trophic Analysis and non-normality. We propose a simple growing network model where the…
Various approaches and measures from network analysis have been applied to granular and particulate networks to gain insights into their structural, transport, failure-propagation and other systems-level properties. In this article, we…
Robust and comprehensive characterization of the topological properties of complex networks requires the adoption of several respective measurements, among which the node degree has special importance. In the present work, we provide an…
The trophic levels of nodes in directed networks can reveal their functional properties. Moreover, the trophic coherence of a network, defined in terms of trophic levels, is related to properties such as cycle structure, stability and…
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…
Measuring the importance of nodes in a network with a centrality measure is a core task in any network application. There are many measures available and it is speculated that many encode similar information. We give an explicit non-linear…
Many complex networks are described by directed links; in such networks, a link represents, for example, the control of one node over the other node or unidirectional information flows. Some centrality measures are used to determine the…
Previous work on undirected small-world networks established the paradigm that locally structured networks tend to have high density of short loops. On the other hand, many realistic networks are directed. Here we investigate the local…
We generate new mathematical tools with which to quantify the macroscopic topological structure of large directed networks. This is achieved via a statistical mechanical analysis of constrained maximum entropy ensembles of directed random…