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ZZ
=
. When
ou
Z
<
i
Z
, the network generated have relatively clear
community structure while the community structure becomes obscure when
+
16
out
in
.
≥
Z
8
out
The benchmark networks are generated with
ou
Z
varying from 0 to 8, each
ou
Z
with 50 networks.
Fig.3 shows the distribution of NMI results of the three algorithms averaged over
100 runs for
ou
Z
ranging from 0 to 8. The difference in the three algorithms increases
when
ou
Z
grows. Random optimization method like MOGA-NET become instable
with the increase of
. On
the contrary, SCPSO can always detect the community structure effectively when
ou
Z
<=6, the NMI value is close to 1.0. When
ou
Z
> 6 and even
ou
Z
=8, the NMI
value achieved by SCPSO is still close to 0.6. It indicates that SCPSO can still find out
some high quality community structure even when the network structure becomes
obscure.
ou
Z
. The performance of GN drop rapidly when
>
Z
5
out
Fig. 3.
The comparison of NMI in synthetic network
Experimental Results and Analysis on Real Networks
Four well studied real-world networks whose community structures are known in prior,
including Zachary's Karate Club [20], Bottlenose Dolphins [21], the American College
Football [5], and the Krebs' topics on American politics [22], are selected as
benchmark networks to verify the performance of SCPSO.
In the experiments on real networks, we run MOGA-NET 100 times over each real
network and calculate the average value of modularity Q and NMI, since MOGA-NET
are random optimization algorithms and the result of each run may be different. In
addition, MOGA-NET is also a multi-objective optimization algorithm and returns a
set of solutions called Pareto front. For the convenience of comparison, the solution
with max modularity Q is selected as the single recommendation solution from the
solution set of MOGA-NET and the corresponding Q and NMI are chosen as the final
result.
