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Spatial Networks

  • Reference work entry
  • First Online:
Encyclopedia of Social Network Analysis and Mining

  • 210 Accesses

Synonyms

Network geography; Space-embedded networks; Transportation systems; Urban networks

Glossary

Graph:

(or Network) A set of vertices connected by edges

Adjacency Matrix:

A matrix A which represents the structure of a graph. The element Aij is either 0 if i and j are not connected or Aij = 1 if there is an edge from i to j. For a spatial network, the position of the nodes {xi} is needed in order to completely characterize the network

Betweenness Centrality:

The betweenness centrality of a vertex (or an edge) x is defined as \( BC(x)={\sum}_{s,t\in V}\frac{\sigma_{st}(x)}{\sigma_{st}} \) where σst(x) is the number of shortest paths between s and t using x and σst is the number of all shortest paths between s and t

Betweenness Centrality Impact:

Measures how a new link affects the average betweenness centrality of a graph. This quantity can help in characterizing the different types of new links during the evolution of a (spatial) network

Cell:

Also called face for planar network is...

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Author information

Authors and Affiliations

  1. Institut de Physique Théorique, CEA, CNRS-URA, 2306, Gif-sur-Yvette, France

    Marc Barthelemy

Authors
  1. Marc Barthelemy
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Corresponding author

Correspondence to Marc Barthelemy .

Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Calgary, Calgary, AB, Canada

    Reda Alhajj

  2. Department of Computer Science, University of Calgary, Calgary, AB, Canada

    Jon Rokne

Section Editor information

  1. Yahoo Inc, London, UK

    Fabrizio Silvestri

  2. University of Calabria, Via Pietro Bucci, 42C, 87036, Arcavacata di Rende, Italy

    Andrea Tagarelli

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Barthelemy, M. (2018). Spatial Networks. In: Alhajj, R., Rokne, J. (eds) Encyclopedia of Social Network Analysis and Mining. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-7131-2_40

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