Discrete Morse theory (Forman, 1998) is the combinatorial analog of classical Morse theory for smooth manifolds. A discrete Morse function assigns values to cells of a simplicial complex such that each cell has at most one lower-dimensional face with a higher value. Critical cells (those with no such "pairing") correspond to topological features: critical 0-cells are minima (components), critical 1-cells are saddles (loops), critical 2-cells are maxima. A discrete gradient vector field pairs non-critical cells, and gradient paths flow between critical cells — collapsing the complex to a minimal CW-complex with the same homotopy type, called the Morse complex.