gives the adjacency matrix of edge weights of the graph g.
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.
Examplesopen allclose all
Basic Examples (2)
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:
Wolfram Research (2010), WeightedAdjacencyMatrix, Wolfram Language function, https://reference.wolfram.com/language/ref/WeightedAdjacencyMatrix.html (updated 2015).
Wolfram Language. 2010. "WeightedAdjacencyMatrix." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/WeightedAdjacencyMatrix.html.
Wolfram Language. (2010). WeightedAdjacencyMatrix. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/WeightedAdjacencyMatrix.html