Row-column visibility graph approach to two-dimensional landscapes

A new concept, called the row-column visibility graph, is proposed to map two-dimensional landscapes to complex networks. A cluster coverage is introduced to describe the extensive property of node clusters on a Euclidean lattice. Graphs mapped from fractals generated with the probability redistribution model behave scale-free. They have pattern-induced hierarchical organizations and comparatively much more extensive structures. The scale-free exponent has a negative correlation with the Hurst exponent, however, there is no deterministic relation between them. Graphs for fractals generated with the midpoint displacement model are exponential networks. When the Hurst exponent is large enough (e.g., H>0.5), the degree distribution decays much more slowly, the average coverage becomes significant large, and the initially hierarchical structure at H<0.5 is destroyed completely. Hence, the row-column visibility graph can be used to detect the pattern-related new characteristics of two-dimensional landscapes.