<p>This study addresses the challenge of efficiently distributing water from a central source to distinct demand points through an irrigation canal system. In this network design, the demand locations serve as network nodes, interconnected by arcs that represent the canals to be built. The building expense for each canal is influenced by various factors, including land structure and topography. The rate of water flow along a canal path from the main source to a specific demand location is restricted by the minimum capacity of the canal along that route. The primary objective is to identify a subset of canals that can maximize water delivery per unit of time to each demand location while minimizing construction costs and satisfying constraints due to canal capacities. The proposed graph-theoretic approach is validated using a semi-real irrigation case study with an irregular, free-form, topology.</p>