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(a)
U.S. Patent at 1985
10
5
10
4
Power
law
10
3
10
2
Giant
connected
component
10
1
10
0
10
0
10
1
10
2
10
3
Component size
10
4
10
5
10
6
(b)
10
6
LinkedIn 2006.08
10
5
10
4
Power
law
10
3
10
2
Giant
connected
component
10
1
10
0
10
0
10
1
10
2
10
3
10
4
10
5
10
6
10
7
Radius
FIGURE 8.20
Size distribution of connected components of (a) U.S. Patent and (b) LinkedIn
graphs. Notice the size of the disconnected components (DCs) follows a power law, which
explains the first peak around radius 0 of the radius plots in Figure 8.18.
Now we can explain the three important areas of Figure 8.18: “
outsiders
” are the
vertices in the disconnected components, and responsible for the first peak and the
negative slope to the dip. “
Core
” are the central vertices with the smallest radii from
the giant connected component. “
Whiskers
” [33] are the vertices connected to the
GCC with long paths.
8.6.4.3 Radius Plot of GCC
Figure 8.16b shows that all vertices of the GCC of the YahooWeb graph have radius
6 or more except for google.com that has radius one.
8.6.4.4 “Core” and “Whisker” Vertices
Figure 8.21 shows the radius-degree plot of Patent, YahooWeb, and LinkedIn graphs.
The radius-degree plot is a scatterplot with one dot for every vertex plotting the
degree of the vertex vs. its radius. The points corresponding to vertices in the GCC
are colored with blue, while the rest is in magenta. We observe that the highest
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