Eigenspaces of Graphs and their Utility
Date:
Abstract: Eigenspaces of linear operators associated with graphs have well known applications in the context of graph partitioning. In this talk, I will use combinatorial methods to evaluate the relationship between eigenvector entries and adjacency structure, particularly in constructing graphs with prescribed eigenvectors. As examples, I will characterize eigenspaces for well-studied graph families including Johnson graphs and perform a similar analysis for graph products. In addition to these combinatorial results, this approach also has applications to dimensionality reduction, a natural problem in data science.