An n-pointed configuration space of a topological space X parametrizes n distinct points in X. Configuration spaces of higher dimensional manifolds have been studied widely, but less is known when X is a graph. We consider a family of graphs $G_n$ with compatible $S_n$-actions. Fixing the number of points k, the homology groups of the k-configuration spaces of these graphs exhibit representation stability for many families. Examples include the star graphs, complete graphs, and the Kneser graphs. Our goal is to explicitly compute these stable representations. We use a discretized model for the configuration spaces developed by Abrams that has a cellular decomposition in terms of the combinatorics of the graphs and we perform our computations in the software system SageMath. We will present some partial results in the cases k=2 and G is a star graph and a complete graph. This is joint work with Eric Ramos.


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