Graph clustering using graph entropy complexity traces

In this paper, we aim to present a principled approach to the problem of depth-based complexity characterisation of graphs. Our idea is to decompose graphs into substructures of increasing size, and then to measure the complexity of these substructures using Shannon entropy or von-Neumann entropy. We commence by identifying the dominant vertex in a graph. From the dominant vertex, we construct subgraphs of increasing K layers, so-called semidiameter subgraphs. We then measure how the entropy varies with increasing K layer semidiameter subgraphs. We construct a vector of subgraph entropies for each graph, a depth-based complexity trace, and then perform graph clustering in the principal components space of the vectors. We explore our approach on both synthetic data and datasets from the domain of bioinformatics.