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dles. Working on shorter EEG epochs will insure the stationarity for the underly-
ing processes and thus any change in the connectivity can be detected. Therefore,
a proper length of EEG epochs has to be determined for measuring the connec-
tivity among EEG recordings. We chose the length of the EEG epochs equal to
10.24 seconds (2048 points), which has also been utilized in many pervious EEG
research studies [11, 12]. The brain connectivity measured using CMI form the
complete graph, in which each node has an arc to every other adjacent vertex. In
the procedure for removing the insignificant arcs (weak connection between brain
regions), we first estimated an appropriate threshold value by utilizing the statisti-
cal tests. We determined this threshold by observing the statical significance over
the complete connectivity graph, this threshold value was set to be a value where
the small noise is eliminated, but yet the real signal is not deleted [5]. Figure 14.5
shows an example of a complete graph and a correspondent graph after edges with
weak connectivity were removed.
Fig. 14.5. (a) A complete connectivity graph (b) After applying the threshold and removing the arcs
with insignificant connectivity
14.4.2.
Maximum Clique Algorithm
We adopted the algorithm to find a maximum clique in the brain connectivity
graph after deleting the insignificant arcs in the original complete graph as fol-
lows: Let
G
=
G
(
V,E
) be a simple, undirected graph where
V
=
}
is the set of vertices (nodes), and
E
denotes the set of arcs. Assume that there
is no parallel arcs (and no self-loops joining the same vertex) in
G
. Denote an
arc joining vertex
i
and
j
by (
i,j
).Wedefine a clique of
G
as a subset
C
of
vertices with the property that every pair of vertices in
C
is connected by an arc;
that is,
C
is a clique if the subgraph
G
(
C
) induced by
C
is complete. Then, the
{
1
,...,n
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