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allshortestpaths (biograph)

Find all shortest paths in biograph object

Syntax

[dist] = allshortestpaths(BGObj)

[dist] = allshortestpaths(BGObj, ...'Directed', DirectedValue, ...)
[dist] = allshortestpaths(BGObj, ...'Weights', WeightsValue, ...)

Arguments

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

Description

[dist] = allshortestpaths(BGObj) finds the shortest paths between every pair of nodes in a graph represented by an N-by-N adjacency matrix extracted from a biograph object, BGObj, using Johnson's algorithm. Nonzero entries in the matrix 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.

[...] = allshortestpaths (BGObj, 'PropertyName', PropertyValue, ...) calls allshortestpaths 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] = allshortestpaths(BGObj, ...'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 sparse matrix being ignored. Default is true.

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

More About

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).

See Also

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