@article{PhillipsSchwanghartHeckmann2015,
  author    = {Phillips, Jonathan D. and Schwanghart, Wolfgang and Heckmann, Tobias},
  title     = {Graph theory in the geosciences},
  series = {Earth science reviews : the international geological journal bridging the gap between research articles and textbooks},
  volume    = {143},
  journal   = {Earth science reviews : the international geological journal bridging the gap between research articles and textbooks},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0012-8252},
  doi       = {10.1016/j.earscirev.2015.02.002},
  pages     = {147 -- 160},
  year      = {2015},
  abstract  = {Graph theory has long been used in quantitative geography and landscape ecology and has been applied in Earth and atmospheric sciences for several decades. Recently, however, there have been increased, and more sophisticated, applications of graph theory concepts and methods in geosciences, principally in three areas: spatially explicit modeling, small-world networks, and structural models of Earth surface systems. This paper reviews the contrasting goals and methods inherent in these approaches, but focuses on the common elements, to develop a synthetic view of graph theory in the geosciences. Techniques applied in geosciences are mainly of three types: connectivity measures of entire networks; metrics of various aspects of the importance or influence of particular nodes, links, or regions of the network; and indicators of system dynamics based on graph adjacency matrices. Geoscience applications of graph theory can be grouped in five general categories: (1) Quantification of complex network properties such as connectivity, centrality, and clustering; (2) Tests for evidence of particular types of structures that have implications for system behavior, such as small-world or scale-free networks; (3) Testing dynamical system properties, e.g., complexity, coherence, stability, synchronization, and vulnerability; (4) Identification of dynamics from historical records or time series; and (5) spatial analysis. Recent and future expansion of graph theory in geosciences is related to general growth of network-based approaches. However, several factors make graph theory especially well suited to the geosciences: Inherent complexity, exploration of very large data sets, focus on spatial fluxes and interactions, and increasing attention to state transitions are all amenable to analysis using graph theory approaches. (C) 2015 Elsevier B.V. All rights reserved.},
  language  = {en}
}
@misc{HeckmannSchwanghartPhillips2015,
  author    = {Heckmann, Tobias and Schwanghart, Wolfgang and Phillips, Jonathan D.},
  title     = {Graph theory-recent developments of its application in geomorphology},
  series = {Geomorphology : an international journal on pure and applied geomorphology},
  volume    = {243},
  journal   = {Geomorphology : an international journal on pure and applied geomorphology},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0169-555X},
  doi       = {10.1016/j.geomorph.2014.12.024},
  pages     = {130 -- 146},
  year      = {2015},
  abstract  = {Applications of graph theory have proliferated across the academic spectrum in recent years. Whereas geosciences and landscape ecology have made rich use of graph theory, its use seems limited in physical geography, and particularly in geomorphology. Common applications of graph theory analyses of connectivity, path or transport efficiencies, subnetworks, network structure, system behaviour and dynamics, and network optimization or engineering all have uses or potential uses in geomorphology and closely related fields. In this paper, we give a short introduction to graph theory and review previous geomorphological applications or works in related fields that have been particularly influential. Network-like geomorphic systems can be classified into nonspatial or spatially implicit system components linked by statistical/causal relationships and spatial units linked by some spatial relationship, for example by fluxes of matter and/or energy. We argue that, if geomorphic system properties and behaviour (e.g., complexity, sensitivity, synchronisability, historical contingency, connectivity etc.) depend on system structure and if graph theory is able to quantitatively describe the configuration of system components, then graph theory should provide us with tools that help in quantifying system properties and in inferring system behaviour. (C) 2015 Elsevier B.V. All rights reserved.},
  language  = {en}
}