Tolerance analysis in scale-free social networks with varying degree exponents

Published date18 March 2019
Date18 March 2019
AuthorKwok Tai Chui,Chien-wen Shen
Subject MatterLibrary & information science,Librarianship/library management,Library technology,Information behaviour & retrieval,Information user studies,Metadata,Information & knowledge management,Information & communications technology,Internet
Tolerance analysis in scale-free
social networks with varying
degree exponents
Kwok Tai Chui
Department of Electronic Engineering, City University of Hong Kong,
Kowloon Tong, Hong Kong, and
Chien-wen Shen
National Central University, Taoyuan City, Taiwan
Purpose There are many complex networks like World-Wide Web, internet and social networks have been
reported to be scale-free. The major property of scale-free networks is their degree distributions are in power
law form. Generally, the degree exponents of scale-free networks fall into the range of (2, 3). The purpose of
this paper is to investigate other situations where the degree exponents may lie outside the range.
Design/methodology/approach In this paper, analysis has been carried out by varying the degree
exponents in the range of (0.5, 4.5). In total, 243 scenarios have been generated with varying network size of
1,000, 2,000 and 4,000, and degree exponents in the range of (0.5, 4.5) using interval of 0.05.
Findings The following five indicators have been investigated: average density, average clustering
coefficient, average path length, average diameter and average node degree. These indicators vary with the
network size and degree exponent. If certain indicators do not satisfy with the user requirement using degree
exponents of (2, 3), one can further increase or decrease the value with tradeoff. Results recommend that for
degree exponents in (0.5, 2), 26 possible scale-free networks can be selected whereas for (3, 4.5), 41 possible
scale-free networks can be selected, assuming a 100 percent deviation on the network parameters.
Originality/value A tolerance analysis is given for the tradeoff and guideline is drawn to help better
design of scale-free network for degree exponents in range of (0.5, 2) and (3, 4.5) using network size 1,000,
2,000 and 4,000. The methodology is applicable to any network size.
Keywords Library networks, Social network, Tolerance analysis, Complex network, Degree exponent,
Scale-free network
Paper type Research paper
1. Introduction
Scale-free networks have gained more and more interest in the light of a research paper by
Barabási and Albert (1999) (Aziz et al., 2016). Many networks were found to be scale-free, for
instance, World-Wide Web (Barnett and Jiang, 2016; Wang et al., 2014), Internet of Things
(Qiu et al., 2017; Guo et al., 2013), e-mail (Portela et al., 2016; Yang and Yang, 2014), wireless
sensor networks (Huang et al., 2017; Peng et al., 2016), crisis informetrics (Hossain et al.,
2015), semantic network (Steyvers and Tenenbaum, 2005), patent litigation (Lee et al., 2017)
and food web (Layman et al., 2015; Navia et al., 2016). They are characterized by the degree
distribution which follows power law in terms of P(k)~k
for large k where gdenotes the
degree exponent of the network. The error and attack on the efficiency of scale-free network
can be found in (Crucitti et al., 2003). In this paper, simulation and analysis have been carried
out with degree exponents 0.5 g4.5 which are 1.5 beyond the typical range of
consideration. Scale-free networks will be generated based on variation of two parameters, n
and g. For network size, the values are 1,000, 2,000 and 4,000 whereas the possible gis set
using 0.05 interval. Thus, 243 cases can be formed. Five common parameters, average
density, average clustering coefficient, average path length, average diameter and average
node degree, are being selected for performance evaluation of the networks. Also, the goal is
to perform tolerance analysis in 0.5 g2 and 3og4.5 in order to explain the tradeoff
when gexceeds the boundary, 2 g3.
Library Hi Tech
Vol. 37 No. 1, 2019
pp. 57-71
© Emerald PublishingLimited
DOI 10.1108/LHT-07-2017-0146
Received 27 July 2017
Revised 3 December 2017
21 April 2018
Accepted 23 May 2018
The current issue and full text archive of this journal is available on Emerald Insight at:
analysis in
scale-free social

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