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graphallshortestpaths

(To be removed) Find all shortest paths in graph

graphallshortestpaths will be removed in a future release. Use distances instead.

Syntax

[dist] = graphallshortestpaths(G)
[dist] = graphallshortestpaths(G, ...'Directed', DirectedValue, ...)
[dist] = graphallshortestpaths(G, ...'Weights', WeightsValue, ...)

Arguments

G N-by-N adjacency matrix that represents a graph. Nonzero entries in matrix G represent the weights of the edges.
DirectedValueProperty that indicates whether the graph is directed or undirected. Enter false for an undirected graph. This results in the upper triangle of the matrix being ignored. Default is true.
WeightsValueColumn vector that specifies custom weights for the edges in matrix G. It must have one entry for every nonzero value (edge) in matrix G. The order of the custom weights in the vector must match the order of the nonzero values in matrix G when it is traversed column-wise. This property lets you use zero-valued weights. By default, graphallshortestpaths gets weight information from the nonzero entries in matrix G.

Description

Tip

For introductory information on graph theory functions, see Graph Theory Functions.

[dist] = graphallshortestpaths(G) finds the shortest paths between every pair of nodes in the graph represented by matrix G, using Johnson's algorithm. Input G is an N-by-N adjacency matrix that represents a graph. Nonzero entries in matrix G represent the weights of the edges.

Output dist is an N-by-N matrix where dist(S,T) is the distance of the shortest path from source node S to target node T. Elements in the diagonal of this matrix are always 0, indicating the source node and target node are the same. A 0 not in the diagonal indicates that the distance between the source node and target node is 0. An Inf indicates there is no path between the source node and the target node.

Johnson's algorithm has a time complexity of O(N*log(N)+N*E), where N and E are the number of nodes and edges respectively.

[...] = graphallshortestpaths (G, 'PropertyName', PropertyValue, ...) calls graphallshortestpaths with optional properties that use property name/property value pairs. You can specify one or more properties in any order. Each PropertyName must be enclosed in single quotes and is case insensitive. These property name/property value pairs are as follows:

[dist] = graphallshortestpaths(G, ...'Directed', DirectedValue, ...) indicates whether the graph is directed or undirected. Set DirectedValue to false for an undirected graph. This results in the upper triangle of the matrix being ignored. Default is true.

[dist] = graphallshortestpaths(G, ...'Weights', WeightsValue, ...) lets you specify custom weights for the edges. WeightsValue is a column vector having one entry for every nonzero value (edge) in matrix G. The order of the custom weights in the vector must match the order of the nonzero values in matrix G when it is traversed column-wise. This property lets you use zero-valued weights. By default, graphallshortestpaths gets weight information from the nonzero entries in matrix G.

References

[1] Johnson, D.B. (1977). Efficient algorithms for shortest paths in sparse networks. Journal of the ACM 24(1), 1-13.

[2] Siek, J.G., Lee, L-Q, and Lumsdaine, A. (2002). The Boost Graph Library User Guide and Reference Manual, (Upper Saddle River, NJ:Pearson Education).

Version History

Introduced in R2006b

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Warns starting in R2022a

Behavior changed in R2021b

See Also