Graphlet and Orbit Computation on Heterogeneous Graphs

Abstract: Many applications, ranging from natural to social sciences, rely on graphlet analysis for the intuitive and meaningful characterization of networks employing micro-level structures as building blocks. However, it has not been thoroughly explored in heterogeneous graphs, which comprise various types of nodes and edges. Finding graphlets and orbits for heterogeneous graphs is difficult because of the heterogeneity and abundance of semantic information. We consider heterogeneous graphs, which can be treated as colored graphs. By applying the canonical label technique, we determine the graph isomorphism problem with multiple states on nodes and edges. With minimal parameters, we build all non-isomorphic graphs and associated orbits. We provide a Python package that can be used to generate orbits for colored directed graphs and determine the frequency of orbit occurrence. Finally, we provide four examples to illustrate the use of the Python package.