Graph theory in the geosciences

Phillips, Jonathan D.; Schwanghart, Wolfgang; Heckmann, Tobias

doi:10.1016/j.earscirev.2015.02.002

Cited by 112 publications

(84 citation statements)

References 123 publications

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“…There are few examples of network or graph-based analyses of evolutionary, developmental, successional or chronosequences in geosciences Phillips et al 2015), However, network-based methods have been applied to identification of key transitions, historical contingency, and memory in time series and historical data in climatology, paleoclimatology, and seismology (Marwan et al 2009;Donges et al 2011;Donner and Donges 2012;Telesca and Lovallo 2012;Radebach 2013). Phillips (2015) analyzed the network of possible pedological transitions revealed in a soil chronosequence via graph theory, but did not analyze the temporal network of transitions.…”

Section: Examplesmentioning

confidence: 99%

Complexity of Earth Surface System Evolutionary Pathways

Phillips

2016

Math Geosci

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Evolution of Earth surface systems (ESS) comprises sequential transitions between system states. Treating these as directed graphs, algebraic graph theory was used to quantify complexity of archetypal structures, and empirical examples of forest succession and alluvial river channel change. Spectral radius measures structural complexity and is highest for fully connected, lowest for linear sequential and cyclic graphs, and intermediate for divergent and convergent patterns. The irregularity index β represents the extent to which a subgraph is representative of the full graph. Fully connected graphs have β = 1. Lower values are found in linear and cycle patterns, while higher values, such as those of divergent and convergent patterns, are due to a few highly connected nodes. Algebraic connectivity (μ(G)) indicates inferential synchronization and is inversely related to historical contingency. Highest values are associated with fully connected and strongly connected mesh graphs, whereas forking structures and linear sequences all have μ(G) = 1, with cycles slightly higher. Diverging vs. converging graphs of the same size and topology have no differences with respect to graph complexity, so complexity change is dependent on whether development results in increased or reduced richness. Convergent-divergent mode switching, however, would generally increase ESS complexity, decrease irregularity, and increase algebraic connectivity. As ESS and associated graphs evolve, none of the possible trends reduces complexity, which can only remain constant or increase. Algebraic connectivity may increase, however. As improving shortcomings in ESS 123 Math Geosci evolution models generally result in elaborating possible state changes, this produces more structurally complex but less historically contingent models.

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Section: Examplesmentioning

confidence: 99%

Complexity of Earth Surface System Evolutionary Pathways

Phillips

2016

Math Geosci

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“…The preponderance of these applications appears to focus on global climate dynamics (Tsonis and Roebber, 2004;Yamasaki et al, 2008;Donges et al, 2009;Martin et al, 2013), with some other examples including studies of hurricanes and earthquakes (e.g., Elsner et al, 2009;Fogarty et al, 2009;Abe and Suzuki, 2004). For a recent review of geoscientific applications of graph theory, see Phillips et al (2015). Narrowing the view to water resource studies, network theory applications have been even more limited to date, though evidently valuable to the extent that they have been conducted.…”

Section: Application To Hydrometric Networkmentioning

confidence: 99%

Complex network theory, streamflow, and hydrometric monitoring system design

Halverson

Fleming

2015

Hydrol. Earth Syst. Sci.

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Abstract. Network theory is applied to an array of streamflow gauges located in the Coast Mountains of British Columbia (BC) and Yukon, Canada. The goal of the analysis is to assess whether insights from this branch of mathematical graph theory can be meaningfully applied to hydrometric data, and, more specifically, whether it may help guide decisions concerning stream gauge placement so that the full complexity of the regional hydrology is efficiently captured. The streamflow data, when represented as a complex network, have a global clustering coefficient and average shortest path length consistent with small-world networks, which are a class of stable and efficient networks common in nature, but the observed degree distribution did not clearly indicate a scale-free network. Stability helps ensure that the network is robust to the loss of nodes; in the context of a streamflow network, stability is interpreted as insensitivity to station removal at random. Community structure is also evident in the streamflow network. A network theoretic community detection algorithm identified separate communities, each of which appears to be defined by the combination of its median seasonal flow regime (pluvial, nival, hybrid, or glacial, which in this region in turn mainly reflects basin elevation) and geographic proximity to other communities (reflecting shared or different daily meteorological forcing). Furthermore, betweenness analyses suggest a handful of key stations which serve as bridges between communities and might be highly valued. We propose that an idealized sampling network should sample high-betweenness stations, small-membership communities which are by definition rare or undersampled relative to other communities, and index stations having large numbers of intracommunity links, while retaining some degree of redundancy to maintain network robustness.

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“…Geomorphic applications of these spectral graph theory methods are reviewed by Heckmann et al (2015) and Phillips et al (2015). Spatially explicit graph and network analysis has been extensively applied to study connectivity in landscape ecology, and has also been applied recently to study geomorphic connectivity in fluvial systems (e.g.…”

Section: Connectivity and Complexitymentioning

confidence: 99%

Geomorphic and hydraulic unit richness and complexity in a coastal plain river

Phillips

2017

Earth Surf Processes Landf

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Geomorphic and hydraulic units in river channels are closely linked to geodiversity and habitats, and thus to biodiversity. In a ~ 200 km reach of the lower Sabine River, in the northern Gulf of Mexico Coastal Plain, 72 different hydraulic units (HU) were identified in six geomorphic zones or river styles. Richness–area relationships indicate a linear or logarithmic increase of HUs, as opposed to the less steep power functions generally found in biogeographic species–area curves or in soil richness–area analyses. Different results are obtained when starting from the upstream or downstream end of the study area, indicating the importance of directionality in such analyses. These results show that HUs (and related habitats and biotopes) are both richer and more variable than a repeated sequence of units. The number of HUs inundated increases linearly with flow stage categories, indicating the importance of high within‐bank flows in maintaining and activating HUs. Aggregated HUs (AHUs) associated with similar geomorphic units are highly connected, both with respect to patterns of spatial adjacency and potential connectivity at similar flow levels. Spectral graph theory metrics applied to a graph representation of spatial adjacency shows a highly complex network with a high potential for rapid propagation of changes—and even more so for a graph based on flow connectivity. The flow connectivity graph shows far higher synchronization as indicated by algebraic connectivity. Thus suggests more rapid and coherent changes for processes driven by river flow, as opposed to phenomena driven by other factors between flow events. These findings have important implications for understanding relationships between geodiversity and habitat diversity, managing habitat and biodiversity, and linking the latter to instream flows. Copyright © 2017 John Wiley & Sons, Ltd.

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Graph theory in the geosciences

Cited by 112 publications

References 123 publications

Complexity of Earth Surface System Evolutionary Pathways

Complexity of Earth Surface System Evolutionary Pathways

Complex network theory, streamflow, and hydrometric monitoring system design

Geomorphic and hydraulic unit richness and complexity in a coastal plain river

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