So I know that the center of mass can be calculated by averaging the vertices of a mesh, but what if the density of vertices is uneven. now I would find the distance between a vertex and it’s neighbors, but how do I proportion this?

Vertex density is not how you would determine an accurate center of mass. Assuming a uniform density, what you need to compute is the *volume* of an object. This is defined by vertices and the topology between them, but it has nothing to do with “the distance between a vertex and it’s neighbors”.