Abstract by Reilly Beckstrand
Equitable Decompositions and the Graph Fourier Transform
The study of networks is a multifaceted and complex field. Much about a networks structure is linked with the spectrum of the eigen values of its (weighted) adjacency matrix. Because eigen values depend on the global structure of the network finding the eigenvalues can be a complex and tedious process, especially as the network size increases. Our research offers a novel way to decompose a network around equitable partitions, a special type of network communities. This method uses Discrete Fourier Transforms and preserves the networks spectra. This method extends and simplified the previous method used to decompose networks.