Can we calculate the dimensionality of some discrete space?

Question

Is it possible to calculate the number of dimensions in some discrete space if we have only a complete scheme of all its points and possible transitions between them? There are no regularities, fractals and the like in its organization. We have access only to an array of points and transitions between them. Such computations can be resource-intensive, so I'm especially looking for algorithms that can quickly estimate the dimensionality of the space based on the available data about the points in the space and their adjacencies. I have looked through the material on discreteness of space (mostly discussions), but have not encountered approaches to dimensioning space where linearly independent vectors are not possible.