For any topological space of n-dimensions, there can only exist topological bases up to that given dimension. For example, a 3D space can only contain β 0 (representing connected components), β 1 (representing holes and cycles), and β 2 (representing voids and cavities) in the space. Figure represents a hydrogen bonding network for an atomistic MD simulation of water as a graph. A graph is a 2D topological space, and thus has a couple of Betti numbers β 0 and β 1 . Figure illustrates that, for a simulation snapshot, the number of connected components is 12, the number of cycles is 2, and thus the EC is