A \(C^*\)-Algebra Construction for Undirected Graphs
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To each undirected graph, we associate an edge-colored directed graph and hence a universal and reduced \(C^*\)-algebra. We then use results on edge-colored directed graphs to completely describe the universal and reduced undirected graph \(C^*\)-algebras in the case of finite graphs. We extend the descriptions of the universal algebra to arbitrary undirected graphs using direct limits.