GraphDistanceMatrix

GraphDistanceMatrix[g]
gives the matrix of distances between vertices for the graph g.

GraphDistanceMatrix[g,d]
gives the matrix of distances between vertices of maximal distance d in the graph g.

GraphDistanceMatrix[{vw,},]
uses rules vw to specify the graph g.

Details and OptionsDetails and Options

  • GraphDistanceMatrix returns a SparseArray object or an ordinary matrix.
  • The entries of the distance matrix dij give the shortest distance from vertex vi to vertex vj.
  • The diagonal entries dii of the distance matrix are always zero.
  • The entry dij is Infinity () if there is no path from vertex vi to vertex vj.
  • In GraphDistanceMatrix[g,d], an entry dij will be Infinity if there is no path from vertex vi to vertex vj in d steps or less.
  • The vertices vi are assumed to be in the order given by VertexList[g].
  • For a weighted graph, the distance is the minimum of the sum of weights along any path from vertex vi to vertex vj.
  • The following options can be given:
  • EdgeWeightAutomaticweight for each edge
    MethodAutomaticmethod to use
  • Possible Method settings include "Dijkstra", "FloydWarshall", and "Johnson".
Introduced in 2010
(8.0)
| Updated in 2015
(10.3)