We have developed a novel method for delineating valley networks on Mars. The valleys are inferred from digital topography by an autonomous computer algorithm as drainage networks, instead of being manually mapped from images. Individual drainage basins are precisely defined and reconstructed to restore flow continuity disrupted by craters. Drainage networks are extracted from their underlying basins using the contributing area threshold method. We demonstrate that such drainage networks coincide with mapped valley networks verifying that valley networks are indeed drainage systems. Our procedure is capable of delineating and analyzing valley networks with unparalleled speed and consistency. We have applied this method to 28 Noachian locations on Mars exhibiting prominent valley networks. All extracted networks have a planar morphology similar to that of terrestrial river networks. They are characterized by a drainage density of ~0.1 km-1, low in comparison to the drainage density of terrestrial river networks. Slopes of streams in Martian valley networks decrease downstream at a slower rate than slopes of streams in terrestrial river networks. This analysis, based on a sizable data set of valley networks, reveals that although valley networks have some features pointing to their origin by precipitation-fed runoff erosion, their quantitative characteristics suggest that precipitation intensity and/or longevity of past pluvial climate were inadequate to develop mature drainage basins on Mars.