WeightedAdjacencyMatrix

WeightedAdjacencyMatrix[g]

gives the adjacency matrix of edge weights of the graph g.

WeightedAdjacencyMatrix[{vw,…}]

uses rules vw to specify the graph g.

Details and Options

  • WeightedAdjacencyMatrix returns a SparseArray object, which can be converted to an ordinary matrix using Normal.
  • An entry wij of the weighted adjacency matrix is the weight of a directed edge from vertex νi to vertex νj. If there is no edge the weight is taken to be 0.
  • An edge without explicit EdgeWeight specified is taken to have weight 1.
  • An undirected edge is interpreted as two directed edges with opposite directions and the same weight.
  • The vertices vi are assumed to be in the order given by VertexList[g].
  • The weighted adjacency matrix for a graph will have dimensions ×, where is the number of vertices.

Examples

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Basic Examples  (2)

The weighted adjacency matrix of an undirected graph:

The weighted adjacency matrix of a directed graph:

Scope  (5)

The weighted adjacency matrix of an undirected graph is symmetric:

The weighted adjacency matrix of a directed graph can be unsymmetric:

Use rules to specify the graph:

The weighted adjacency matrix of the graph with self-loops has diagonal entries:

WeightedAdjacencyMatrix works with large graphs:

Use MatrixPlot to visualize the matrix:

Properties & Relations  (4)

Rows and columns of the weighted adjacency matrix follow the order given by VertexList:

Use WeightedAdjacencyGraph to construct a graph from a weighted adjacency matrix:

The number of rows or columns is equal to the number of vertices:

The main diagonals for a loop-free graph are all zeros:

Wolfram Research (2010), WeightedAdjacencyMatrix, Wolfram Language function, https://reference.wolfram.com/language/ref/WeightedAdjacencyMatrix.html (updated 2015).

Text

Wolfram Research (2010), WeightedAdjacencyMatrix, Wolfram Language function, https://reference.wolfram.com/language/ref/WeightedAdjacencyMatrix.html (updated 2015).

CMS

Wolfram Language. 2010. "WeightedAdjacencyMatrix." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/WeightedAdjacencyMatrix.html.

APA

Wolfram Language. (2010). WeightedAdjacencyMatrix. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/WeightedAdjacencyMatrix.html

BibTeX

@misc{reference.wolfram_2024_weightedadjacencymatrix, author="Wolfram Research", title="{WeightedAdjacencyMatrix}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/WeightedAdjacencyMatrix.html}", note=[Accessed: 23-April-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_weightedadjacencymatrix, organization={Wolfram Research}, title={WeightedAdjacencyMatrix}, year={2015}, url={https://reference.wolfram.com/language/ref/WeightedAdjacencyMatrix.html}, note=[Accessed: 23-April-2024 ]}