# conncomp

Connected graph components

## Description

returns the connected components of
graph `bins`

= conncomp(`G`

)`G`

as bins. The bin numbers indicate which component each
node in the graph belongs to.

If

`G`

is an undirected graph, then two nodes belong to the same component if there is a path connecting them.If

`G`

is a directed graph, then two nodes belong to the same strong component only if there is a path connecting them in both directions.

uses additional options specified by one or more Name-Value pair arguments. For
example, `bins`

= conncomp(`G`

,`Name,Value`

)`conncomp(G,'OutputForm','cell')`

returns a cell array to
describe the connected components.

## Examples

### Find Graph Components

Create and plot an undirected graph with three connected components. Use `conncomp`

to determine which component each node belongs to.

G = graph([1 1 4],[2 3 5],[1 1 1],6); plot(G)

bins = conncomp(G)

`bins = `*1×6*
1 1 1 2 2 3

### Strong and Weak Graph Components

Create and plot a directed graph, and then compute the strongly connected components and weakly connected components. Weakly connected components ignore the direction of connecting edges.

s = [1 2 2 3 3 3 4 5 5 5 8 8]; t = [2 3 4 1 4 5 5 3 6 7 9 10]; G = digraph(s,t); plot(G,'Layout','layered')

str_bins = conncomp(G)

`str_bins = `*1×10*
4 4 4 4 4 6 5 1 3 2

weak_bins = conncomp(G,'Type','weak')

`weak_bins = `*1×10*
1 1 1 1 1 1 1 2 2 2

### Discard Graph Components Based on Size

Use the second output of `conncomp`

to extract the largest component of a graph or to remove components below a certain size.

Create and plot a directed graph. The graph has one large component, one small component, and several components that contain only a single node.

s = [1 2 2 3 3 3 4 5 5 5 8 8 9]; t = [2 3 4 1 4 5 5 3 6 7 9 10 10]; G = digraph(s,t,[],20); plot(G,'Layout','layered')

Calculate the weakly connected components and specify two outputs to `conncomp`

to get the size of each component.

[bin,binsize] = conncomp(G,'Type','weak')

`bin = `*1×20*
1 1 1 1 1 1 1 2 2 2 3 4 5 6 7 8 9 10 11 12

`binsize = `*1×12*
7 3 1 1 1 1 1 1 1 1 1 1

Use `binsize`

to extract the largest component from the graph. `idx`

is a logical index indicating whether each node belongs to the largest component. The `subgraph`

function extracts the nodes selected by `idx`

from `G`

.

idx = binsize(bin) == max(binsize); SG = subgraph(G, idx); plot(SG)

A similar use of `binsizes`

is to filter out components based on size. The procedure is similar to extracting the largest component, however in this case each node can belong to any component that meets the size requirement.

Filter out any components in `G`

that have fewer than 3 nodes. `idx`

is a logical index indicating whether each node belongs to a component with 3 or more nodes.

idx = binsize(bin) >= 3; SG = subgraph(G, idx); plot(SG)

## Input Arguments

### Name-Value Arguments

Specify optional pairs of arguments as
`Name1=Value1,...,NameN=ValueN`

, where `Name`

is
the argument name and `Value`

is the corresponding value.
Name-value arguments must appear after other arguments, but the order of the
pairs does not matter.

*
Before R2021a, use commas to separate each name and value, and enclose*
`Name`

*in quotes.*

**Example: **`bins = conncomp(G,'OutputForm','cell')`

`OutputForm`

— Type of output

`'vector'`

(default) | `'cell'`

Type of output, specified as the comma-separated pair consisting of
`'OutputForm'`

and either
`'vector'`

or `'cell'`

.

Option | Output |
---|---|

`'vector'` (default) | `bins` is a numeric vector
indicating which connected component each node belongs
to. |

`'cell'` | `bins` is a cell array, and
`bins{j}` contains the node IDs for
all nodes that belong to component
`j` . |

`Type`

— Type of connected components

`'strong'`

(default) | `'weak'`

**Note**

The `'Type'`

option is supported only for
directed graphs created using `digraph`

.

Type of connected components, specified as the comma-separated pair
consisting of `'Type'`

and either
`'strong'`

(default) or
`'weak'`

.

Option | Result |
---|---|

`'strong'` (default) | Two nodes belong to the same connected component only
if there is a path connecting them in
both directions. |

`'weak'` | Two nodes belong to the same connected component if there is a path connecting them, ignoring edge directions. |

**Example: **`bins = conncomp(G,'Type','weak')`

computes
the weakly connected components of directed graph
`G`

.

## Output Arguments

`bins`

— Connected components

vector | cell array

Connected components, returned as a vector or cell array. The bin numbers assign each node in the graph to a connected component:

If

`OutputForm`

is`'vector'`

(default), then`bins`

is a numeric vector indicating which connected component (bin) each node belongs to.If

`OutputForm`

is`'cell'`

, then`bins`

is a cell array, with`bins{j}`

containing the node IDs for all nodes that belong to component`j`

.

`binsizes`

— Size of each connected component

vector

Size of each connected component, returned as a vector.
`binsizes(i)`

gives the number of elements in component
`i`

. The length of `binsizes`

is equal
to the number of connected components, `max(bins)`

.

## More About

### Weakly Connected Components

Two nodes belong to the same weakly connected component if there is a path connecting them (ignoring edge direction). There are no edges between two weakly connected components.

The concepts of strong and weak components apply only to directed graphs, as they are equivalent for undirected graphs.

### Strongly Connected Components

Two nodes belong to the same strongly connected component if there are paths connecting them in both directions. There can be edges between two strongly connected components, but these connecting edges are never part of a cycle.

The bin numbers of strongly connected components are such that any edge connecting two components points from the component of smaller bin number to the component with a larger bin number.

The concepts of strong and weak components apply only to directed graphs, as they are equivalent for undirected graphs.

## Extended Capabilities

### C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

The name-value argument

`'OutputForm','cell'`

that specifies cell array output is not supported.

### Thread-Based Environment

Run code in the background using MATLAB® `backgroundPool`

or accelerate code with Parallel Computing Toolbox™ `ThreadPool`

.

## Version History

**Introduced in R2015b**

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