Image Processing Reference
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at Fig.1 and Fig.2, respectively. Modularity maximization here reveals 4 communities shown
by different colors. However, the multi-communities membership results in overlapping
communities illustrated by overlapping ovals (Fig.1).
For example, according to modality
maximization,
the node 1 belongs to community c 2 ,
but it also has links to all other
communities indicated by blue bars at Fig.2.
Participation of different nodes in selected communities is presented at Fig.3 and Fig.4. These
graphs show that even if a node is assigned by some community detection algorithm to a
certain community, it still may have significant membership in other communities. This
multi-communities membership is one of the reasons why different algorithms disagree
on communities partitions. In practice, e.g., in targeted advertisements, due to the "hard"
decision in community detection, some users may be missed even if they are strongly related
to the targeted group. For example, user '29' is assigned to c 3 (Fig.1), but it also has equally
strong memberships in c 2 and c 4 (Fig.3). Using soft community detection user '29' can also be
qualified for advertisements targeted to c 2 or c 4 .
Fig. 1. Overlapping communities in karate club.
Fig. 2. Membership weight distribution for selected users in karate club social network.
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