Fully-Dynamic Hierarchical Graph Clustering Using Cut Trees

Algorithms or target functions for graph clustering rarely admit quality guarantees or optimal results in general. However, a hierarchical clustering algorithm by Flake et al., which is based on minimum s-t-cuts whose sink sides are of minimum size, yields such a provable guarantee. We introduce a new degree of freedom to this method by allowing arbitrary minimum s-t-cuts and show that this unrestricted algorithm is complete, i.e., any clustering hierarchy based on minimum s-t-cuts can be found by choosing the right cuts. This allows for a more comprehensive analysis of a graph’s structure. Additionally, we present a dynamic version of the unrestricted approach which employs this new degree of freedom to maintain a hierarchy of clusterings fulfilling this quality guarantee and effectively avoid changing the clusterings.