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The von Neumann Theil index: Characterizing graph centralization using the von Neumann index

Abstract:

We show that the von Neumann entropy (from herein referred to as the von Neumann index) of a graph’s trace normalized combinatorial Laplacian provides structural information about the level of centralization across a graph. This is done by considering the Theil index, which is an established statistical measure used to determine levels of inequality across a system of ‘agents’, e.g., income levels across a population. Here, we establish a Theil index for graphs, which provides us with a macro...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Accepted Manuscript

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Publisher copy:
10.1093/comnet/cnx061

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Institution:
University of Oxford
Division:
MPLS Division
Department:
Engineering Science
Oxford college:
Oriel College
Role:
Author
ORCID:
0000-0002-9623-5087
Publisher:
Oxford University Press Publisher's website
Journal:
Journal of Complex Networks Journal website
Volume:
6
Issue:
6
Pages:
859–876
Publication date:
2018-01-24
Acceptance date:
2017-12-06
DOI:
EISSN:
2051-1329
ISSN:
2051-1310
Pubs id:
pubs:813431
URN:
uri:ada29d6b-07eb-4c24-a9f2-eb9a538c7d8c
UUID:
uuid:ada29d6b-07eb-4c24-a9f2-eb9a538c7d8c
Local pid:
pubs:813431

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