Given an aperture distribution for a single fracture, a graph theory model has been employed to simulate the transport properties of the fracture. In the processes of imbibition and drainage, the connectivity of each phase at a particular capillary pressure can be sought out by the priority-first search algorithm of graph theory. Then, the flow path in each phase can be identified, and flow equations can be established and solved in an optimal manner. It was observed that in a simulated rough fracture, a few flow ''channels'' can dominate the permeability of the whole system. ¿ American Geophysical Union 1995