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One issue that is not addressed in [
4
] pertains to the selection of parameters
m
and
e
.
Setting a high value for
e
(the maximum possible value for
e
is 1.0) will render the
core detection step very eclectic, i.e., few (
m
,
e
)-cores will be detected. Moreover,
higher values for
will also result in the detection of fewer cores (for instance, all
nodes with degree lower than
m
will be excluded from the core selection process).
For this reason, we employed an iterative scheme [
17
], in which the community
seed set selection operation is carried out multiple times with different values of
m
m
so that a meaningful subspace of these two parameters is thoroughly
explored and the respective (
and
e
m
,
e
)-cores are detected.
m
e
) parameter space is carried out as depicted in
Fig.
5.3
. We start by a very high value for both parameters. Since the maximum
possible values for
The exploration of the (
,
are
k
max
(maximum degree on the graph) and 1.0,
respectively, we start the parameter exploration by two values close to them (for
instance, we could select
m
and
e
0.9; the results of the algorithm
are not very sensitive to this choice). We identify the respective (
m
0
¼
0.9
k
max
and
e
0
¼
) cores and
associated core sets and then relax the parameters in the following way. First, we
reduce
m
,
e
m
; if it falls below a certain threshold (e.g.,
m
min
¼
4), we then reduce
e
by a
small step (e.g., 0.05) and we reset
m ¼ m
0
. When both
m
and
e
reach a small value
(
e ¼ e
min
), we terminate the community seed set detection step. This
exploration path ensures that first high-quality communities will be discovered and
subsequently less profound ones will also be detected. Although the parameter
sampling process is depicted as linear in Fig.
5.3
, in practice one could employ a
near-logarithmic sampling scheme for parameter
m ¼ m
min
and
m
in order to save computational
cost.
Fig. 5.3 Depiction of the (
m
,
e
) parameter space exploration path
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