  A class of networks are those with both positive and negative links. In this
manuscript, we studied the interplay between positive and negative ties on
mesoscopic level of these networks, i.e., their community structure. A
community is considered as a tightly interconnected group of actors; therefore,
it does not borrow any assumption from balance theory and merely uses the
well-known assumption in the community detection literature. We found that if
one detects the communities based on only positive relations (by ignoring the
negative ones), the majority of negative relations are already placed between
the communities. In other words, negative ties do not have a major role in
detecting communities of studied signed networks. Moreover, regarding the
internal negative ties, we proved that most unbalanced communities are
maximally balanced, and hence they cannot be partitioned into k nonempty
sub-clusters with higher balancedness (k >= 2). Furthermore, we showed that
although the mediator triad ++- (hostile-mediator-hostile) is underrepresented,
it constitutes a considerable portion of triadic relations among communities.
Hence, mediator triads should not be ignored by community detection and
clustering algorithms. As a result, if one uses a clustering algorithm that
operates merely based on social balance, mesoscopic structure of signed
networks significantly remains hidden.
