Structure of isotropic and anisotropic graph in ArcView and AccessMod. (A) Isotropic analysis case based on slopes derived from a DEM (values are in meters and cell width is 1 km). The largest slope between one cell and all its neighboring cells is attributed to the focal cell. The lines linking pairs of cells depict the direction of largest slope. The "travelling time without slope consideration" is obtained by considering a walking individual travelling at 5 km/h on flat ground. The "travelling time using largest slope" uses the largest slope values and correct travelling speeds through the Tobler formula (see text). (B) In the anisotropic analysis, slopes are computed between each cell and all its neighbors, and slope values are attributed to the arcs linking all pairs of cells. The directional slopes shown in the graph are computed from the center cell to its eight neighbors (using the same DEM than in (A)). The travelling times using directional slopes are derived using the Tobler formula, and can be either computed "from" the center cell or "toward" the center cell. (C) DEM used in the example; (D) population grid used in the example; (E) extent of a catchment area computed through four different ways of considering slopes. Numbers in brackets specify the population covered by each corresponding catchment.