# Hierarchy measures in complex networks.

@article{Trusina2004HierarchyMI, title={Hierarchy measures in complex networks.}, author={Ala Trusina and Sergei Maslov and Petter Minnhagen and Kim Sneppen}, journal={Physical review letters}, year={2004}, volume={92 17}, pages={ 178702 } }

Using each node's degree as a proxy for its importance, the topological hierarchy of a complex network is introduced and quantified. We propose a simple dynamical process used to construct networks which are either maximally or minimally hierarchical. Comparison with these extremal cases as well as with random scale-free networks allows us to better understand hierarchical versus modular features in several real-life complex networks. For random scale-free topologies the extent of topological… Expand

#### 136 Citations

Hierarchical Characterization of Complex Networks

- Mathematics, Physics
- 2006

The current work considers the concept of virtual hierarchies established around each node and the respectively defined hierarchical node degree and clustering coefficient, complemented by new hierarchical measurements, in order to obtain a powerful set of topological features of complex networks. Expand

Hierarchy Measure for Complex Networks

- Physics, Medicine
- PloS one
- 2012

This work develops an approach and proposes a quantity (measure) which is simple enough to be widely applicable, reveals a number of universal features of the organization of real-world networks and is capable of capturing the essential Features of the structure and the degree of hierarchy in a complex network. Expand

Interplay Between Hierarchy and Centrality in Complex Networks

- Computer Science
- IEEE Access
- 2020

Results show that network density and transitivity play a key role in shaping the redundancy between centrality and hierarchy measures. Expand

Degree correlations in growing networks with deletion of nodes

- Mathematics
- 2008

In this paper we study the degree distribution and the two-node degree correlations in growing networks generated via a general linear preferential attachment of new nodes together with a uniformly… Expand

Degree landscapes in scale-free networks.

- Mathematics, Physics
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2006

To quantify the topology, this work measures the widths of the mountains and the separation between different mountains to model networks organized under constraints imposed by the space the networks are embedded in, associated to spatial or in molecular networks to functional localization. Expand

Graph hierarchy: a novel framework to analyse hierarchical structures in complex networks

- Medicine
- Scientific reports
- 2021

A hierarchical framework which can be defined on any simple graph is introduced and several metrics, including hierarchical levels, a generalisation of the notion of trophic levels, influence centrality, a measure of a vertex’s ability to influence dynamics, and democracy coefficient, an measure of overall feedback in the system are developed. Expand

The effects of degree correlations on network topologies and robustness

- Computer Science
- 2007

It is shown that to some extent, the characteristic path length, clustering coefficient, modular extent and robustness of networks are directly influenced by the degree correlation. Expand

Generating Hierarchically Modular Networks via Link Switching

- Computer Science
- ArXiv
- 2009

This paper introduces a method to generate hierarchically modular networks with prescribed node degree list by link switching that utilizes a user-specified topology to determine relatedness between pairs of nodes in terms of edge distances. Expand

Random walk hierarchy measure: What is more hierarchical, a chain, a tree or a star?

- Computer Science, Physics
- Scientific reports
- 2015

The novelty of this approach is that directed trees corresponding to multi level pyramidal structures obtain higher hierarchy scores compared to directed chains and directed stars, and in the thermodynamic limit the hierarchy measure of regular trees is converging to a well defined limit depending only on the branching number. Expand

Hierarchy in directed random networks: analytical and numerical results

- Computer Science, Physics
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2013

It is shown that the hierarchical structure can be drastically different if there are one-point correlations in the network and there is an optimal level of nonzero correlations maximizing the level of hierarchy. Expand

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