Hierarchical link clustering algorithm in networks.

Hierarchical network clustering is an approach to find tightly and internally connected clusters (groups or communities) of nodes in a network based on its structure. Instead of nodes, it is possible to cluster links of the network. The sets of nodes belonging to clusters of links can overlap. While overlapping clusters of nodes are not always expected, they are natural in many applications. Using appropriate dissimilarity measures, we can complement the clustering strategy to consider, for example, the semantic meaning of links or nodes based on their properties. We propose a new hierarchical link clustering algorithm which in comparison to existing algorithms considers node and/or link properties (descriptions, attributes) of the input network alongside its structure using monotonic dissimilarity measures. The algorithm determines communities that form connected subnetworks (relational constraint) containing locally similar nodes with respect to their description. It is only implicitly based on the corresponding line graph of the input network, thus reducing its space and time complexities. We investigate both complexities analytically and statistically. Using provided dissimilarity measures, our algorithm can, in addition to the general overlapping community structure of input networks, uncover also related subregions inside these communities in a form of hierarchy. We demonstrate this ability on real-world and artificial network examples.