conncomp (biograph)
(Removed) Find strongly or weakly connected components in biograph object
Syntax
[
S
, C
]
= conncomp(BGObj
)
[S
, C
]
= conncomp(BGObj
, ...'Directed', DirectedValue
,
...)
[S
, C
]
= conncomp(BGObj
, ...'Weak', WeakValue
,
...)
Arguments
BGObj
| Biograph object created by biograph (object
constructor). |
DirectedValue | Property that indicates whether the graph is directed or undirected.
Enter false for an undirected graph. This results in
the upper triangle of the adjacency matrix being ignored. Default is
true . A DFS-based algorithm computes the
connected components. Time complexity is |
WeakValue | Property that indicates whether to find weakly connected components
or strongly connected components. A weakly connected component is a
maximal group of nodes that are mutually reachable by violating the edge
directions. Set WeakValue to
true to find weakly connected components. Default
is false , which finds strongly connected components.
The state of this parameter has no effect on undirected graphs because
weakly and strongly connected components are the same in undirected
graphs. Time complexity is O(N+E) , where
N and E are number of nodes
and edges respectively. |
Description
Tip
For introductory information on graph theory functions, see Graph Theory Functions.
[
finds the strongly connected components of an N-by-N adjacency matrix extracted from a
biograph object, S
, C
]
= conncomp(BGObj
)BGObj
using Tarjan's algorithm. A strongly
connected component is a maximal group of nodes that are mutually reachable without
violating the edge directions. The N-by-N adjacency matrix represents a directed graph;
all nonzero entries in the matrix indicate the presence of an edge.
The number of components found is returned in S
, and
C
is a vector indicating to which component each node
belongs.
Tarjan's algorithm has a time complexity of O(N+E)
, where
N
and E
are the number of nodes and edges
respectively.
[
calls
S
, C
] =
conncomp(BGObj
,
...'PropertyName
',
PropertyValue
, ...)conncomp
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 is directed or undirected. Set
S
, C
]
= conncomp(BGObj
, ...'Directed', DirectedValue
,
...)DirectedValue
to false
for an
undirected graph. This results in the upper triangle of the adjacency matrix being
ignored. Default is true
. A DFS-based algorithm computes the
connected components. Time complexity is O(N+E)
, where
N
and E
are number of nodes and edges
respectively.
[
indicates whether to find weakly connected components or strongly connected components.
A weakly connected component is a maximal group of nodes that are mutually reachable by
violating the edge directions. Set S
, C
]
= conncomp(BGObj
, ...'Weak', WeakValue
,
...)WeakValue
to
true
to find weakly connected components. Default is
false
, which finds strongly connected components. The state of
this parameter has no effect on undirected graphs because weakly and strongly connected
components are the same in undirected graphs. Time complexity is
O(N+E)
, where N
and E
are
number of nodes and edges respectively.
Note
By definition, a single node can be a strongly connected component.
Note
A directed acyclic graph (DAG) cannot have any strongly connected components larger than one.
References
[1] Tarjan, R.E., (1972). Depth first search and linear graph algorithms. SIAM Journal on Computing 1(2), 146–160.
[2] Sedgewick, R., (2002). Algorithms in C++, Part 5 Graph Algorithms (Addison-Wesley).
[3] 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).