ABSTRACTOne of the most fundamental ways in which ice sheet erosion modifies the topography is by altering the valley pattern. It is assumed that purely fluvial valley systems are dendritic in pattern. This presumably represents the pre-glacial state. Purely alpine glaciation will tend to retain the dendritic system, whereas if active ice sheets take over, the landscape will become progressively modified by multiple watershed breaching, so that the valleys become increasingly inter-connected. This assumption is tested by using topological measures of network connectivity, applied to the valley pattern of Scotland. Several areas in West Greenland and British Columbia are used for comparison. The most suitable measure of network connectivity appears to be theα-index. Values in Scotland range from 0 % (indicating a wholly dendritic pattern) in the southeast of the country to>7 % around the southwestern Great Glen and in Wester Ross. The results seem to fit what is known about the pattern of glaciation from other evidence, though some interesting problem areas like the Glenshiel district are revealed. Mountainous islands which develop their own radial system of ice outflow have prevented the mainland ice from altering their valley pattern and so retain the low values ofαassociated with alpine glaciation. Results from West Greenland and British Columbia fall within the same range.Areas of total glaciation intensity are also derived from a combination of theα-index and the percentage of alpine type valley heads in each area. High intensity corrie glaciation and ice-sheet modification are not necessarily mutually exclusive.