Information Technology Reference
In-Depth Information
Fig. 13.6.
The power-law degree distribution of virtual user network (a) and the
reconstruct network (b)
Table 13.4.
The Number of communities
Month Feb. Mar. Apr. May. Jun. Jun.
NC
a
87 145 99 159 122 139
VN
b
115 179 155 172 195 179
a
The number of well-defined communities.
b
The number of nodes of the largest connected component.
subfigures. It is shown that, the numbers of nodes and edges are very small so
that the network characteristics are not comprehensive analyzed with a too small
threshold selection.
In the case of the basis threshold 0.0010, since the numbers of nodes and edges
of the whole network are all large, there are an obvious differences although the
degrees of nodes is with great changes, which is shown as the last subfigure. For
example, the degree ratio of the node that its identification is 200623 accounts
for the seventh place, but with the decreasing threshold, the ratio value changes
very small and it does not appear the set of the first ten nodes. This case about
the node is the same as node 192562 and node 75415. So the numbers of nodes
and edges have increased substantially due to the distance threshold is selected
too large. Thereby, the changes of degrees of these nodes are hidden and the
accurately community structure can not be obtained according to the topology
of the reconstructed network.
The changes of the ratios of these node degrees are very little when the basis
threshold is 0.0007 or 0.0008. From the Table 13.3, when the threshold is selected
this two values, the proportions of the numbers of nodes and edges of largest con-
nected component to that of the whole network are 80% and 99%, respectively.
Since the threshold selection directly influences the topology of the reconstructed
network, the appropriate distance threshold can be as an important coecient
of the Laplace matrix spectral decomposition algorithm of community finding.
