Graph Similarity based on Graph Fourier Distances

Graph theory is a branch of mathematics which is gaining momentum in the signal processing community due to their ability to efficiently represent data defined on irregular domains. Quantifying the similarity between two different graphs is a crucial operation in many applications involving graphs, such as pattern recognition or social networks' analysis. This paper focuses on the graph similarity problem from the emerging graph Fourier domain, leveraging the spectral decomposition of the Laplacian matrices. In particular, we focus on the intuition that similar graphs should provide similar frequency representation for a particular graph signal. Similarly, we argue that the frequency responses of a particular graph filter applied to two similar graphs should be also similar. Supporting results based on numerical simulations support the aforementioned hypothesis and show that the proposed graph distances provide a new tool for comparing graphs in the frequency domain.