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

Clicked: 5358

Citations: Bibtex RefMan EndNote GB/T7714

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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author="Raf Guns, Ronald Rousseau",

journal="Frontiers of Information Technology & Electronic Engineering",

volume="16",

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year="2015",

publisher="Zhejiang University Press & Springer",

doi="10.1631/FITEE.1400425"

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

%A Raf Guns

%A Ronald Rousseau

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%I Zhejiang University Press & Springer

%DOI 10.1631/FITEE.1400425

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T1 - Unnormalized and normalized forms of gefura measures in directed and undirected networks

A1 - Raf Guns

A1 - Ronald Rousseau

J0 - Frontiers of Information Technology & Electronic Engineering

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EP - 320

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PB - Zhejiang University Press & Springer

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DOI - 10.1631/FITEE.1400425

**Abstract: **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.

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