Tree-like patterns appear in many domains of physics and the quantitative description of their morphology raises an interesting problem. To analyze their topological structure, we introduce combinatorial concepts, the bifurcation and length ratios and the ramification matrix, which generalize ideas originating in hydrogeology. Two-dimensional diffusion-limited aggregation (DLA) patterns are studied along these lines, and their statistical combinatorial properties are compared to those of random and growing binary trees and to experimental data for injection of water in clay.