SpatialMeasures v.0.2 - Continuous average Straightness for spatial graphs

Vincent Labatut (1)

1 LIA - Laboratoire Informatique d'Avignon

This set of R scripts was designed to process several variants of the Straightness (aka. Directness and probably other names): the ratio of the Euclidean to the graph distance. It is a measure designed to study spatial graphs, i.e. graphs embedded in an Euclidean space (nodes have spatial positions, links have spatial length, etc.). First, this toolbox can process the Straightness using the traditional approach, i.e. considering only paths connecting two nodes. It can process the Straightness between two specific nodes, or the Straightness averaged over certain pairs of nodes in the graph (including all pairs). Second, this toolbox can also compute the average Straightness through a continuous approach (by opposition to the discrete traditional approach), and incidentally this is the point of the article cited in the readme. The Straightness is generalized to deal with point-to-point paths, i.e. paths connecting a location on a link to another such position (by opposition to nodes, which are necessarily located on the ends of links). Based on this, we can average the Straightness by integration over the link. This allows deriving the following continuous average variants: Average Straightness between a point and an link (or rather: all the points on this link); Average Straightness between a point and the rest of the graph (or rather: all the points constituting this graph); Average Straightness between two links (or rather: all pairs of points located on these links, each point being on a different one); Average Straightness between a link and the rest of the graph (or rather: all the points located on the link on one side, and all the points constituting the graph on the other side); and Average Straightness over the graph (or rather: between all the pairs of points constituting the graph). Besides the functions used to process the average measures themselves, the scripts also allow to replicate the different experiments conducted in the mentioned article.

Mots clés: Spatial graph; Graph characterization; Centrality measure; Straightness

Domaines: Réseaux sociaux et d'information [cs.SI]; Statistiques [math.ST]; Mathématique discrète [cs.DM]

Vincent Labatut. SpatialMeasures v.0.2 - Continuous average Straightness for spatial graphs. 2016, ⟨swh:1:dir:bbc03899df671a2eaae6b3f98413e30be630ed79;origin=https://hal.archives-ouvertes.fr/hal-02180337;visit=swh:1:snp:464f10366fe1816fbbaf1c328075bd20bd29c36b;anchor=swh:1:rev:8cb7d8d43822b5e121c124c7cb691375e6bab903;path=/⟩. ⟨hal-02180337⟩