Let me be more specific: If $A=BC$, where $A$ and $C$ are given [**Laplacian matrices**](https://en.wikipedia.org/wiki/Laplacian_matrix), how to calculate $B$?

Note that $A, B, C$ are all **square matrices**. I **don't** want numerical solutions. There may be many solutions to this problem, so is there a formulated way to find **one** of them?