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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Approximate von Neumann entropy for directed graphs

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Ye, Cheng [1] ; Wilson, Richard C. [1] ; Comin, Cesar H. [2] ; Costa, Luciano da F. [2] ; Hancock, Edwin R. [1]
Total Authors: 5
[1] Univ York, Dept Comp Sci, York YO10 5GH, N Yorkshire - England
[2] Univ Sao Paulo, Inst Phys Sao Carlos, BR-13560970 Sao Paulo - Brazil
Total Affiliations: 2
Document type: Journal article
Source: Physical Review E; v. 89, n. 5 MAY 12 2014.
Web of Science Citations: 20

In this paper, we develop an entropy measure for assessing the structural complexity of directed graphs. Although there are many existing alternative measures for quantifying the structural properties of undirected graphs, there are relatively few corresponding measures for directed graphs. To fill this gap in the literature, we explore an alternative technique that is applicable to directed graphs. We commence by using Chung's generalization of the Laplacian of a directed graph to extend the computation of von Neumann entropy from undirected to directed graphs. We provide a simplified form of the entropy which can be expressed in terms of simple node in-degree and out-degree statistics. Moreover, we find approximate forms of the von Neumann entropy that apply to both weakly and strongly directed graphs, and that can be used to characterize network structure. We illustrate the usefulness of these simplified entropy forms defined in this paper on both artificial and real-world data sets, including structures from protein databases and high energy physics theory citation networks. (AU)

FAPESP's process: 12/50986-7 - Graph spectra and complex network evolution
Grantee:Luciano da Fontoura Costa
Support type: Regular Research Grants
FAPESP's process: 11/22639-8 - Unveiling the relationship between structure and dynamics on modular networks
Grantee:Cesar Henrique Comin
Support type: Scholarships in Brazil - Doctorate
FAPESP's process: 11/50761-2 - Models and methods of e-Science for life and agricultural sciences
Grantee:Roberto Marcondes Cesar Junior
Support type: Research Projects - Thematic Grants