Abstract A topographic surface can be modeled as a graph, a visibility graph in terms of how each point location is visible to every other. This paper demonstrates various structural properties of visibility patterns with a topographic surface from a graph perspective, which could be important for landscape planning. This paper illustrates the fact that the visibility graph with a topographic surface is a small-world. This finding implies that the average visual separation between any two point locations with a surface is very short (i.e. a small separation), and the visible locations to a given location have a high possibility of being visible to each other (i.e. a high clustering level). Additionally we show that the visibility graph exhibits an exponential distribution rather than a power law distribution, i.e. it is not scale-free, in contrast to many other real world networks.