Describing classes of graphs that optimize a function of the eigenvalues subject to some constraints is one of the topics addressed by Spectral Graph Theory (SGT). In this paper, we propose RioGraphX, a science gateway developed on top of Apache Spark, which aims to obtain all graphs that optimize a given mathematical function of the eigenvalues of a graph. Initial experiments involving small graphs have pointed out optimal graphs in a reasonable computational time, and also have shown that leveraging parallel processing is a promising approach to handle larger graphs.