Measuring distances among graphs en route to graph clustering

The graph data structure offers a highly expressive way of representing many real-world constructs such as social networks, chemical compounds, the world wide web, street maps, etc. In essence, any collection of entities and the relationships between them can be modelled using a graph, thus preserving more information about the real-world objects than a simple vector space model. An issue that arises when operating on collections of graphs, however, is that most statistical analysis and machine learning methods expect their input data to be in the form of multidimensional vectors, where all items can be compared with each other using well-understood metrics such as Euclidean or Manhattan distance. This paper presents a variety of approaches for computing distances between graphs with known node correspondence, with the aim of applying those measures alongside clustering algorithms to discover patterns in a given dataset. The performance of each distance measure is then evaluated through its ability to identify communities of graphs with similar features. We show that because the considered distance metrics highlight different structural properties, the method that produces the highest quality result will depend on the characteristics of the processed graph population.