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Marc Barthelemy1,2, Geoff Boeing3, Alain Chiaradia4

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New tools analyze elevation changes in surfacic networks, revealing how "excess effort" on shortest paths (SPs) follows a power law. This impacts urban and transport network analysis.

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Area of Science:

  • Complex systems analysis
  • Network science
  • Geographic information science

Background:

  • Surfacic networks, like transportation and urban systems, are built on 2D manifolds.
  • Node elevation fluctuations create deviations from planar networks, necessitating specialized analytical tools.

Purpose of the Study:

  • To introduce novel metrics for analyzing elevation impacts on surfacic networks.
  • To investigate how elevation changes influence network properties, particularly shortest paths and centrality.

Main Methods:

  • Development of metrics: lazy paths, graph arduousness, and excess effort.
  • Application of metrics to toy models and empirical analysis of urban pedestrian networks.
  • Examination of elevation's effect on betweenness centrality distribution.

Main Results:

  • Excess effort along shortest paths exhibits a non-universal power law distribution.
  • Elevation changes significantly impact the spatial distribution of betweenness centrality.
  • Steep slopes are probable along shortest paths irrespective of start/end elevation differences.

Conclusions:

  • Elevation fluctuations are critical factors shaping surfacic network characteristics.
  • The developed tools provide a framework for analyzing complex surface-constrained systems.
  • Findings have implications for urban planning, transportation logistics, and network design.