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. 
[
determines the
singlesource shortest paths from node dist
, path
, pred
] = shortestpath(BGObj
, S
)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 Inf
s 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.
[
determines
the single sourcesingle destination shortest path from node dist
, path
, pred
] = shortestpath(BGObj
, S
, T
)S
to
node T
.
[...] = shortestpath(..., '
calls PropertyName
', PropertyValue
, ...)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:
indicates whether the graph
represented by the NbyN adjacency matrix extracted from a biograph
object, [...] = shortestpath(..., 'Directed',
DirectedValue
, ...)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
.
lets you specify the algorithm
used to find the shortest path. Choices are:[...] = shortestpath(..., 'Method',
MethodValue
, ...)
'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.
lets you specify custom weights
for the edges. [...] = shortestpath(..., 'Weights',
WeightsValue
, ...)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).
allshortestpaths
 biograph
 conncomp
 graphshortestpath
 isdag
 isomorphism
 isspantree
 maxflow
 minspantree
 topoorder
 traverse