Information Technology Reference
In-Depth Information
Now we demonstrate the validity of the evaluation criterion of community
finding according to the topology structure of the BBS poster networks.
According to Equation (13.1), if the topology of a complex network obeys the
power-law degree distribution, it is approximately a slope line in the log-log plot.
As shown in Figure 13.6(a), the degree distribution of the BBS poster network
has a power-law distribution approximately and its exponent
λ
=1
.
35. Since
the power-law exponent has the range of 1
<λ<
2, the number of well-defined
communities have the hundred order of magnitude according to the evaluation
criterion. The number of well-defined communities of the largest connected com-
ponents each month and the number of nodes of the largest community are listed
in Table 13.4. The number of communities obtained by community finding algo-
rithm has the same magnitude order as the number indicated by the power-law
exponents of the networks each month.
In addition, although there are lots of well-defined communities in the BBS
networks, comparing the data of Table 13.4 with Table 13.2, the number of nodes
contained in the largest connected component is very large. It shows that there
exists a small quantity of hot-topic talks each month on the BBS forum.
The topology of the reconstructed network has exhibited scale-free property
and its power-law exponent is
λ
=1
.
36, which is shown in Figure 13.6(b). This
exponent is quietly closed to the original exponent 1.35, which verifies the second
condition of the evaluation criterion. We calculate the three network centrality
indices of the original network and the reconstructed network, which are shown
in Figure 13.7. We can find that the two curves have no much difference, and
there is an incremental trend of these indexes from Feb. to Jul. Since the network
Fig. 13.7.
The Three network centrality indices comparisons of the original networks
(solid lines) to the reconstructed networks (dotted lines)
