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Youtube). Table 3.1 shows the average path lengths, diameters, and radius for the
four social networks. In absolute terms, the path lengths and diameters for all four are
remarkably short. Interestingly, despite being comparable in size to the Web graph
we considered, the social networks have significantly shorter average path lengths
and diameters. his property may again result from the high degree of reciprocity
within them. Incidentally, Broder et al. [26] noted that if the Web were treated as an
undirected graph, the average path length would drop from 16.12 to 7.
3.2.1.3 Reciprocity
Ali-Hasan and Adamic [19] analyzed the reciprocity of three types of link (blogroll
links, citation links, and comment links) based on the data of three blog commu-
nities (Kuwait, UAE, DFW), and the results in Table 3.2 show a high degree of
reciprocity in all three communities, but the level varied by the type of link. In all
three communities, a greater fraction of blogroll links are reciprocated than post
citations, possibly because blogroll links are more numerous in our data set, and
bloggers sometimes reciprocate blogroll links merely as a courtesy. Furthermore,
reciprocal blogroll links indicate possibly only a mutual awareness, whereas recip-
rocal post citations imply a greater level of interaction, both blogs actively discuss-
ing or linking to one another in their posts rather than one blog simply finding
Table 3.1
AveragePathLength,Radius,andDiameterofthe
StudiedNetworks
Network
Avg. Path Length
Radius
Diameter
Web
16.12
475
905
Flickr
5.67
13
27
LiveJournal
5.88
12
20
Orkut
4.25
6
9
Youtube
5.10
13
21
Table 3.2
PercentageofLinksThatAre
Reciprocated
Kuwait
UAE
DFW
Postcitations
19%
16%
26%
Blogrolllinks
32%
43%
27%
Comments
43%
N/A
N/A
 
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