Full Text:   <1091>

Summary:  <481>

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: 2016

Citations:  Bibtex RefMan EndNote GB/T7714

 ORCID:

Raf Guns

http://orcid.org/0000-0003-3129-0330

Ronald Rousseau

http://orcid.org/0000-0002-3252-2538

-   Go to

Article info.
Open peer comments

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

http://doi.org/10.1631/FITEE.1400425


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.

@article{title="Unnormalized and normalized forms of gefura measures in directed and undirected networks",
author="Raf Guns, Ronald Rousseau",
journal="Frontiers of Information Technology & Electronic Engineering",
volume="16",
number="4",
pages="311-320",
year="2015",
publisher="Zhejiang University Press & Springer",
doi="10.1631/FITEE.1400425"
}

%0 Journal Article
%T Unnormalized and normalized forms of gefura measures in directed and undirected networks
%A Raf Guns
%A Ronald Rousseau
%J Frontiers of Information Technology & Electronic Engineering
%V 16
%N 4
%P 311-320
%@ 2095-9184
%D 2015
%I Zhejiang University Press & Springer
%DOI 10.1631/FITEE.1400425

TY - JOUR
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
VL - 16
IS - 4
SP - 311
EP - 320
%@ 2095-9184
Y1 - 2015
PB - Zhejiang University Press & Springer
ER -
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.

有向网络和无向网络中桥接(gefura)测度的非归一化和归一化形式

目的:针对现实生活中某些网络节点属于预先定义的小组而常规网络其中心性测度并未考虑到这一结构特点,本文以桥接测度作为小组间中介节点的指标并研究之。
创新点:系统性研究非归一化桥接测度,提出除“结构化”归一化(组级别)之外“基本”归一化(节点级别)也是可行的。将无向网络视为对称有向网络,将桥接测度定义推广至有向网络。
方法:首先系统性研究有向网络中的非归一化桥接测度。然后研究有向网络中的归一化桥接测度,指出除“结构化”归一化(组级别)之外,“基本”归一化(节点级别)也是可行的。将无向网络视为对称有向网络,所得结论对于无向网络同样成立。最后,说明如何调节Brandes算法使之应用于测量所提网络的中介中心性。
结论:对于研究复杂网络的社会学家、信息计量学者等,若其所研究的网络被分割为小组,则桥接测度将是十分有用的工具。

关键词:细分为组的网络;分割;桥接(gefura)测度;Q-测度;中介角色;有向网络和无向网络;Brandes算法

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

Reference

[1]Atkin, R.H., 1972. From cohomology in physics to q-connectivity in social science. Int. J. Man-Mach. Stud., 4(2):139-167.

[2]Barrat, A., Barthélemy, M., Pastor-Satorras, R., et al., 2004. The architecture of complex weighted networks. PNAS, 101(11):3747-3752.

[3]Boccaletti, S., Bianconi, G., Criado, R., et al., 2014. The structure and dynamics of multilayer networks. Phys. Rep., 544(1):1-122.

[4]Brainard, W.C., Tobin, J., 1968. Econometric models: their problems and usefulness. Pitfalls in financial model building. Amer. Econ. Rev., 58(2):99-122.

[5]Brandes, U., 2001. A faster algorithm for betweenness centrality. J. Math. Sociol., 25(2):163-177.

[6]Brandes, U., 2008. On variants of shortest-path betweenness centrality and their generic computation. Soc. Netw., 30(2):136-145.

[7]Burt, R.S., 2004. Structural holes and good ideas. Amer. J. Sociol., 110(2):349-396.

[8]Chen, L.X., Rousseau, R., 2008. Q-measures for binary divided networks: bridges between German and English institutes in publications of the J. Fluid Mech. Scientometr., 74(1):57-69.

[9]Christensen, C., Albert, R., 2007. Using graph concepts to understand the organization of complex systems. Int. J. Bifurc. Chaos, 17(7):2201-2214.

[10]Ding, Y., 2011. Scientific collaboration and endorsement: network analysis of coauthorship and citation networks. J. Inform., 5(1):187-203.

[11]Flom, P.L., Friedman, S.R., Strauss, S., et al., 2004. A new measure of linkage between two sub-networks. Connections, 26(1):62-70.

[12]Freeman, L.C., 1977. A set of measures of centrality based on betweenness. Sociometry, 40(1):35-41.

[13]Freeman, L.C., Borgatti, S.P., White, D.R., 1991. Centrality in valued graphs: a measure of betweenness based on network flow. Soc. Netw., 13(2):141-154.

[14]Gould, R.V., Fernandez, R.M., 1989. Structures of mediation: a formal approach to brokerage in transaction networks. Sociol. Method., 19:89-126.

[15]Guimerà, R., Amaral, L.A.N., 2005. Functional cartography of complex metabolic networks. Nature, 433:895-900.

[16]Guimerà, R., Mossa, S., Turtschi, A., et al., 2005. The worldwide air transportation network: anomalous centrality, community structure, and cities’ global roles. PNAS, 102(22):7794-7799.

[17]Guns, R., Liu, Y.X., 2010. Scientometric research in China in context of international collaboration. Proc. 6th Int. Conf. on Scientometrics and University Evaluation, p.112-115.

[18]Guns, R., Rousseau, R., 2009. Gauging the bridging function of nodes in a network: Q-measures for networks with a finite number of subgroups. Proc. 12th ISSI, p.131-142.

[19]Guns, R., Liu, Y.X., Mahbuba, D., 2011. Q-measures and betweenness centrality in a collaboration network: a case study of the field of informetrics. Scientometrics, 87(1):133-147.

[20]Liu, Y.X., Guns, R., Rousseau, R., 2013. A binary tree as a basic model for studying hierarchies using Q-measures. SRELS J. Inform. Manag., 50(5):521-528.

[21]Newman, M.E.J., Girvan, M., 2004. Finding and evaluating community structure in networks. Phys. Rev. E, 69:026113.1-026113.15.

[22]Otte, E., Rousseau, R., 2002. Social network analysis: a powerful strategy, also for the information sciences. J. Inform. Sci., 28(6):441-453.

[23]Rousseau, R., 2005. Q-measures for binary divided networks: an investigation within the field of informetrics. Proc. Amer. Soc. Inform. Sci. Technol., 42(1):675-696.

[24]Rousseau, R., Zhang, L., 2008. Betweenness centrality and Q-measures in directed valued networks. Scientometrics, 75(3):575-590.

[25]Rousseau, R., Liu, Y.X., Guns, R., 2013. Mathematical properties of Q-measures. J. Inform., 7(3):737-745.

[26]Rousseau, R., Liu, Y.X., Guns, R., 2014. An addendum and correction to “Mathematical properties of Q-measures” (vol. 7, issue 3, pp.737-745). J. Inform., 8(3):486-490.

[27]Rousseau, R., Guns, R., Liu, Y.X., 2015. Gauging the bridging function of nodes in a network: the gefura measure. Proc. 8th Int. Conf. on Scientometrics and University Evaluation, in press.

[28]Sakai, T., 2007. On the reliability of information retrieval metrics based on graded relevance. Inform. Process. Manag., 43(2):531-548.

[29]Wasserman, S., Faust, K., 1994. Social Network Analysis: Methods and Applications. Cambridge University Press, UK.

[30]Zhang, W.L., Yin, L.C., Pang, J., 2009. The application of Q-measure to gender study in cooperation network. Sci. Technol. Progr. Pol., 26(15):100-103 (in Chinese).

Open peer comments: Debate/Discuss/Question/Opinion

<1>

Please provide your name, email address and a comment





Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - Journal of Zhejiang University-SCIENCE