Spherical averaging operators are ubiquitous, appearing in solutions to the wave equation, inverse problems, and point configuration questions. Results on L^{p} improving estimates for the spherical averaging operator in the continuous setting have been studied classically by Littman and Strichartz in the 1970s. In contrast, it is only recently that l^{p} improving results have been obtained in the discrete setting for the spherical averaging operator. These ideas can be used to study multilinear geometric averaging operators motivated by Falconer type problems and how the underlying graph structure of the point configuration impacts the mapping properties of the operators. I am working on a study of averaging operators based on connected graphs over the integers and seeking to understand how graph structure of the underlying configuration impacts mapping properties.