Moses Boudourides and Gerasimos Antypas (2002) 'A Simulation of the Structure of the World-Wide Web'
Sociological Research Online, vol. 7, no. 1, <http://www.socresonline.org.uk/7/1/boudourides.html>
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Received: 9/8/2001 Accepted: 7/5/2002 Published: 31/5/2002
X' = X + (Xlnk - X)(1 - m)/2,where m is a value between zero and one, which increases randomly but monotonically for each successive link.
|a||Probability threshold to introduce new web sites||0.2|
|ß||Probability threshold to introduce new topics||0.5|
|y||Probability threshold to increase the number of new web pages||0.0025|
|T||Total number of topics||200|
|p1||Probability threshold to introduce a link with a page of the same topic||0.5|
|p2||Probability threshold to introduce a link with a page of a different topic||0.0005|
|Animation 1. Web pages generation every 25 time units|
|Figure 1: The simulation output|
|Figure 2: Cumulative web pages per time unit|
|Figure 3: Out-going links per web page|
|Figure 4: In-coming links per web page|
|Figure 5: Links per web page|
|Figure 6 Web pages per web site|
|Number of Web Pages||Simulation||Distribution|
|18 or more||13||19|
pn = an-ke-n/g,where a, k, g are the parameters. In our simulation, we have used a least square optimisation in order to evaluate these parameters and we have found them to take the following values:
a = 128.4421
k = 0.0783
g = 5.1872
|Figure 7: Web pages per web site|
|Figure 8: Probability distribution of links|
2The authors wish to thank the referees of the paper for providing useful suggestions on the sociological discussion of the Web.
3This is the initiative of the 'semantic web' currently launched by the World-Wide Web Consortium (W3C). According to Berners-Lee, Handler & Lassila (2001): "The Semantic Web is an extension of the current web in which information is given well-defined meaning, better enabling computers and people to work in cooperation".
4 Unintended or unanticipated consequences (Merton, 1936) are of tremendous interest to sociologists in the tradition of Merton's (1963) discussions of manifest versus latent functions of purposive action. They also play a central role in more recent sociological developments such as Giddens's (1984) structuration theory.
5This is the dogma of the 'Actor Network Theory,' in which the development and stabilisation of scientific and technological objects (facts and artefacts) results from the construction of heterogeneous networks as concrete alignments between human actors, natural phenomena, and social or technical intervening aspects (Callon, 1986; Latour, 1987). However, not everybody would subscribe to these ideas; for some this is a controversial theory and sometimes serious objections are risen against it (Collins, 1994).
6Albert et al. (1999) have estimated the degree of connectivity of the web concluding that any two web pages are separated by an average of '19 clicks.'
7We are tempted to call 'infene' this quantum of information captured by web pages in analogy with Gilbert's neologism.
8 The Matlab program of this simulation is available online at: <http://nicomedia.math.upatras.gr/simulations/ssweb.m>
9 The results of the sensitivity analysis to the variation of the simulation parameters are given in the following table:
|a||ß||y||T||p1||p2||Average number of links||Clustering coefficient||Number of pages||Number of sites|
10 Exponentially truncated powers laws have been used by Newman (2000) in a study of scientific co-authorship networks.
11Although it appears as a disparity in our simulation's computation (y = 2.3637 for out-going links and y = 2.3641 for in-coming links) in contrast with what Barabási & Albert (1999) have found (? = 2.45 for out-going links and y = 2.1 for in-coming links), we must stress the fact that our simulation is based on a rather simplistic model of the real Web, while Barabási & Albert have collected information about a large sample of the real Web composed of over 800 million web pages. What is important is that the results of a simple simulation as ours are exhibiting the same structure with that of the real World-Wide Web: the connectivities of the simulated web pages follow too a scale-free power-law distribution.
12 Again the reason that our simulation has resulted a different value of average path length d than what was computed by Albert, Jeong & Barabási (1999) is due to the fact that our simulation was based on a rather simplistic model of the World-Wide Web, while Albert et al. had focused on a very large sample of the real Web. However, it is in both cases the comparison with the corresponding random graph that implies the property of the small-world.
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