The Wolfram Model is a candidate for the fundamental theory of physics. It proposes hypergraphs as constituents of space while causal evolution of hypergraphs, or causal graphs, as spacetime. By discretizing spacetime, this model hopes to bridge general relativity and quantum mechanic. If hypergraphs and causal graphs are the forms of space and spacetime, they should recover our physical world in the continuous limit; in particular, this project focuses on how geodesics in causal graphs converge to the continuous geodesics. How the size of the graph and the number of graphs averaged affect the speed of convergence? How fast does geodesics within the light-cone converge compared to geodesics on the light-cone? Is it possible to determine the dimension of the manifold using light cones composed from individual geodesics? What are the obstructions and instability of convergence? These are questions this project aims to answer eventually (upon future updates).