The universal graph is a theoretical construct capturing the idea that every aspect of reality can be modeled as a graph composed of vertices and edges and, as such, reality is a graph. From the physical world of atoms, people, and galaxies to the mental planes of thoughts, words, and knowledge, there exists a universal graph hosting all such structures. While this idea is enticing, there are still strides to be made in coming to terms with a reality that is not composed of atoms bound by spacetime, but instead, a graph composed of vertices united by edges. This letter presents three open problems in our understanding of the universal graph.