  Many approaches have been proposed to discover clusters within networks.
Community finding field encompasses approaches which try to discover clusters
where nodes are tightly related within them but loosely related with nodes of
other clusters. However, a community network configuration is not the only
possible latent structure in a graph. Core-periphery and hierarchical network
configurations are valid structures to discover in a relational dataset. On the
other hand, a network is not completely explained by only knowing the
membership of each node. A high level view of the inter-cluster relationships
is needed. Blockmodelling techniques deal with these two issues. Firstly,
blockmodelling allows finding any network configuration besides to the
well-known community structure. Secondly, blockmodelling is a summary
representation of a network which regards not only membership of nodes but also
relations between clusters. Finally, a unique summary representation of a
network is unlikely. Networks might hide more than one blockmodel. Therefore,
our proposed problem aims to discover a secondary blockmodel representation of
a network that is of good quality and dissimilar with respect to a given
blockmodel. Our methodology is presented through two approaches, (a) inclusion
of cannot-link constraints and (b) dissimilarity between image matrices. Both
approaches are based on non-negative matrix factorisation NMF which fits the
blockmodelling representation. The evaluation of these two approaches regards
quality and dissimilarity of the discovered alternative blockmodel as these are
the requirements of the problem.
