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centrality indices have no significant changes before and after community finding
of the network, the algorithm basis on Laplace matrix spectral decomposition
satisfies the third condition of evaluation criterion. In addition, the trend implies
that some central posters have a higher popularity than other general posters
and their articles attract lots of replied articles month by month.
In a word, for the algorithm basis Laplace matrix spectral decomposition,
the three conditions of evaluation criterion of community finding algorithm are
satisfied well according to the data of the BBS poster networks. Hence, the
evaluation criterion of community finding algorithm is validated.
13.6
Future Studies
Further study mainly focuses on two aspects: the community finding algorithm
based on scale-free topology of complex networks and the evaluation criterion of
community finding. Although lots of real-world complex networks have a scale-
free topology structure, the inherent evolving mechanisms forming this special
nature in these networks are to be further thinking and excavated. If the evolu-
tion of complex network is considered as a reverse process of community finding,
the mechanisms of evolution accords with the key rules of community finding
algorithm in the sense. On the other hand, the seeking of evolving mechanisms
is the basis of the analysis of network topologies.
Degree distribution is one of important topology characteristics of complex
network, but there are many other characteristics, such as average shortest path
length, clustering coecient, etc., that be introduced to design some new com-
munity finding algorithms of complex networks. And the centrality indices, such
as betweenness, degree, have introduced to the algorithm of community finding
and some valuable results have obtained by many researchers. So we can ex-
pect that, there are many more centrality indices that can be used to design
community finding algorithms.
In the community finding algorithm based on Laplace matrix spectral decom-
position, we focus on the method of threshold selection of Euclidean distance.
And the method relies mainly on the ratios of nodes and edges of the largest
connected component to those of the whole network. Since the number of com-
munities is obtained before the Euclidean distances between nodes are calcu-
lated, and it is also an important coecient of distance calculation formula, the
relationship between the number of communities and the method of selection
threshold is worth studying further.
For the evaluation criterion of community finding algorithm, lots of existed
results have focused on the complexity of runtime to measure the advantages and
disadvantages of an algorithm. And there are some other simple evaluation crite-
rions. For example, if an algorithm can be validated by some real-world networks,
such as Zachary network, whose community structures are known in advance or
those topologies are very simple, it is an effective one. In the past literature,
there is no use of the network topology to evaluate the algorithm of community
finding. We have mainly adopted the relationship between the power-law expo-
