Patterns of intraspecific genetic variation result from interactions among both historical and contemporary evolutionary processes. Traditionally, population geneticists have used methods such as F-statistics, pairwise isolation by distance models, spatial autocorrelation and coalescent models to analyses this variation and to gain insight about causal evolutionary processes. Here we introduce a novel approach (Population Graphs) that focuses on the analysis of marker-based population genetic data within a graph theoretic framework. This method can be used to estimate traditional population genetic summary statistics, but its primary focus is on characterizing the complex topology resulting from historical and con- temporary genetic interactions among populations. We introduce the application of Population Graphs by examining the range-wide population genetic structure of a Sonoran Desert cactus (Lophocereus schottii). With this data set, we evaluate hypotheses regarding historical vicariance, isolation by distance, population-level assignment and the importance of specific populations to species-wide genetic connectivity. We close by discussing the applicability of Population Graphs for addressing a wide range of population genetic and phylogeographical problems.