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CLC number: TP393; G350

On-line Access: 2015-04-03

Received: 2014-12-09

Revision Accepted: 2015-03-12

Crosschecked: 2015-03-13

Cited: 2

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Citations:  Bibtex RefMan EndNote GB/T7714


Raf Guns


Ronald Rousseau


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Frontiers of Information Technology & Electronic Engineering  2015 Vol.16 No.4 P.311-320


Unnormalized and normalized forms of gefura measures in directed and undirected networks

Author(s):  Raf Guns, Ronald Rousseau

Affiliation(s):  Institute for Education and Information Sciences, University of Antwerp, Venusstraat 35, Antwerp B-2000, Belgium; more

Corresponding email(s):   raf.guns@uantwerpen.be, ronald.rousseau@kuleuven.be, ronald.rousseau@uantwerpen.be

Key Words:  Networks subdivided in groups, Partitions, Gefura measures, Q-measures, Brokerage role, Directed and undirected networks, Brandes’, algorithm

Raf Guns, Ronald Rousseau. Unnormalized and normalized forms of gefura measures in directed and undirected networks[J]. Frontiers of Information Technology & Electronic Engineering, 2015, 16(4): 311-320.

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A1 - Raf Guns
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DOI - 10.1631/FITEE.1400425

In some networks nodes belong to predefined groups (e.g., authors belong to institutions). Common network centrality measures do not take this structure into account. gefura measures are designed as indicators of a node’s brokerage role between such groups. They are defined as variants of betweenness centrality and consider to what extent a node belongs to shortest paths between nodes from different groups. In this article we make the following new contributions to their study: (1) We systematically study unnormalized gefura measures and show that, next to the ‘structural’ normalization that has hitherto been applied, a ‘basic’ normalization procedure is possible. While the former normalizes at the level of groups, the latter normalizes at the level of nodes. (2) Treating undirected networks as equivalent to symmetric directed networks, we expand the definition of gefura measures to the directed case. (3) It is shown how brandes’; algorithm for betweenness centrality can be adjusted to cover these cases.

This article presents a variant of betweenness centrality, gefura measures in undirected networks and adapted to directed networks. Based on the work of Brandes, the paper also proposes an efficient algorithm which is introduced to calculate unnormalized or basic gefura measures in undirected and directed networks. The proposed method is important for network study and with potential application in various fields related to network. The paper is well developed.




Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


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