Hot off the press--more fun with graph theory!
Phillips, J.D. 2016. Identifying sources of soil landscape complexity with spatial adjacency graphs. Geoderma 267: 58-64.
Abstract: Soil landscapes often exhibit complex spatial patterns, with some aspects of soil variation apparently unrelated to measurable variations in environmental controls. However, these local, contingent complexities are not truly random or intrinsically unknowable. The purpose of this work is to develop and apply a method for identifying or teasing out causes of soil landscape complexity. Soil spatial adjacency graphs (SAG) represent the geography of soil landscapes as a network that can be analyzed using algebraic graph theory. These SAGs include linear sequential subgraphs that represent sequences of soil forming factors. The number and length of these soil factor sequences (SFS), and their associated spectral radius values, determine whether the SFS are sufficient to explain the spatial pattern of soil adjacency. SAGs and associated graph theory methods provide useful tools for guiding pedological investigations and identifying gaps in knowledge. The methods also allow sources of soil landscape complexity and variability to be determined in a way that can help assess the underlying deterministic sources of chaos and dynamical instability in pedology. The approach is applied to a soil landscape in central Kentucky, producing a SAG with 13 nodes (soil types) and 36 links indicating whether the soils occur contiguously. Five SFS were identified, the sum of whose spectral radius values is 6.35. The spectral radius of the SAG is 6.56, indicating that the SFS can explain most, but not all, of the complexity of the soil relationships. The analysis also points to potential environmental controls that could potentially enable full explanation.