Image Processing Reference
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recommendation in the phone-calls network according S ( ii )
CC (
)
is shown by the blue arrow
at Fig.12. Scaled pair-wise correlations between oscillators for the whole phone-call network
k , n
Fig. 16. Phone-call network: averaged pair-wise correlations (scaled by 10) between
oscillators at t =10, coupling scenario B.3.
Fig. 17. Phone-call network: averaged pair-wise correlations re-ordered according to
detected communities.
at Fig.12 are shown at Fig.16. Correlations between nodes, re-ordered according to one of the
stable partitions detected by the random walk at t=10 , reveal clearly the community structure
(Fig.17). The phone-calls adjacency matrix (red circles) and all possible intra-community links
(yellow squares) for the stable communities at t
10 are depicted at Fig.18 (a). Links
predicted by system dynamics (blue dots) inside and outside of yellow squares indicate
predicted intra-community and inter-communities connections at different resolution levels
and show the priority of the intra-community connections (Fig.18 (b) - Fig.18(c) ). As the
whole, the presented results for the coupled dynamical systems provide the formal basis for
the recommendation rules formulated in Section 4.2.
As it is shown in Section 3, the dynamical process of opinions convergence may be seen as
the first-order approximation of the network synchronization. At the same time, S ( i , i )
=
CC (
k , n
)
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