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Solve shortest path problem in biograph object
[dist, path, pred] = shortestpath(BGObj, S)
[dist, path, pred] = shortestpath(BGObj, S, T)
[...] = shortestpath(..., 'Directed', DirectedValue, ...)
[...] = shortestpath(..., 'Method', MethodValue, ...)
[...] = shortestpath(..., 'Weights', WeightsValue, ...)
BGObj  Biograph object created by biograph (object constructor). 
S  Node in graph represented by an NbyN adjacency matrix extracted from a biograph object, BGObj. 
T  Node in graph represented by an NbyN adjacency matrix extracted from a biograph object, BGObj. 
DirectedValue  Property that indicates whether the graph represented by the NbyN adjacency matrix extracted from a biograph object, BGObj, 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. 
MethodValue  String that specifies the algorithm used to find the shortest
path. Choices are:

WeightsValue  Column vector that specifies custom weights for the edges in the NbyN adjacency matrix extracted from a biograph object, BGObj. It must have one entry for every nonzero value (edge) in the NbyN adjacency matrix. The order of the custom weights in the vector must match the order of the nonzero values in the NbyN adjacency matrix when it is traversed columnwise. This property lets you use zerovalued weights. By default, shortestpaths gets weight information from the nonzero entries in the NbyN adjacency matrix. 
Tip For introductory information on graph theory functions, see Graph Theory Functions. 
[dist, path, pred] = shortestpath(BGObj, S) determines the singlesource shortest paths from node S to all other nodes in the graph represented by an NbyN adjacency matrix extracted from a biograph object, BGObj. Weights of the edges are all nonzero entries in the NbyN adjacency matrix. dist are the N distances from the source to every node (using Infs for nonreachable nodes and 0 for the source node). path contains the winning paths to every node. pred contains the predecessor nodes of the winning paths.
[dist, path, pred] = shortestpath(BGObj, S, T) determines the single sourcesingle destination shortest path from node S to node T.
[...] = shortestpath(..., 'PropertyName', PropertyValue, ...) calls shortestpath 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:
[...] = shortestpath(..., 'Directed', DirectedValue, ...) indicates whether the graph
represented by the NbyN adjacency matrix extracted from a biograph
object, BGObj, 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.
[...] = shortestpath(..., 'Method', MethodValue, ...) lets you specify the algorithm used to find the shortest path. Choices are:
'BellmanFord' — Assumes weights of the edges to be nonzero entries in the NbyN adjacency matrix. Time complexity is O(N*E), where N and E are the number of nodes and edges respectively.
'BFS' — Breadthfirst search. Assumes all weights to be equal, and nonzero entries in the NbyN adjacency matrix to represent edges. Time complexity is O(N+E), where N and E are the number of nodes and edges respectively.
'Acyclic' — Assumes the graph represented by the NbyN adjacency matrix extracted from a biograph object, BGObj, to be a directed acyclic graph and that weights of the edges are nonzero entries in the NbyN adjacency matrix. Time complexity is O(N+E), where N and E are the number of nodes and edges respectively.
'Dijkstra' — Default algorithm. Assumes weights of the edges to be positive values in the NbyN adjacency matrix. Time complexity is O(log(N)*E), where N and E are the number of nodes and edges respectively.
[...] = shortestpath(..., '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 NbyN 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 NbyN adjacency matrix when it is traversed columnwise. This property lets you use zerovalued weights. By default, shortestpath gets weight information from the nonzero entries in the NbyN adjacency matrix.
[1] Dijkstra, E.W. (1959). A note on two problems in connexion with graphs. Numerische Mathematik 1, 269–271.
[2] Bellman, R. (1958). On a Routing Problem. Quarterly of Applied Mathematics 16(1), 87–90.
[3] Siek, J.G., Lee, LQ, and Lumsdaine, A. (2002). The Boost Graph Library User Guide and Reference Manual, (Upper Saddle River, NJ:Pearson Education).
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