# `connected_components`

    // named parameter version
    template <class VertexListGraph, class ComponentMap, class P, class T, class R>
    typename property_traits<ComponentMap>::value_type
    connected_components(VertexListGraph& G, ComponentMap comp,
        const bgl_named_params<P, T, R>& params = all defaults);

    // there is not a non-named parameter version of this function

The `connected_components()` functions compute the connected components of an undirected graph using a DFS-based approach. A connected component of an undirected graph is a set of vertices that are all reachable from each other. If the connected components need to be maintained while a graph is growing the disjoint-set based approach of function `incremental_components()` is faster. For ``static'' graphs this DFS-based approach is faster [8].

The output of the algorithm is recorded in the component property map `comp`, which will contain numbers giving the component number assigned to each vertex. The total number of components is the return value of the function.

### Where Defined

`boost/graph/connected_components.hpp`

### Parameters

IN: `const Graph& g`

> An undirected graph. The graph type must be a model of Vertex List Graph and Incidence Graph.
> Python: The parameter is named `graph`.

OUT: `ComponentMap c`

> The algorithm computes how many connected components are in the graph, and assigning each component an integer label. The algorithm then records which component each vertex in the graph belongs to by recording the component number in the component property map. The `ComponentMap` type must be a model of Writable Property Map. The value type should be an integer type, preferably the same as the `vertices_size_type` of the graph. The key type must be the graph's vertex descriptor type.
> Python: Must be an `vertex_int_map` for the graph.
> Python default: `graph.get_vertex_int_map("component")`

### Named Parameters

UTIL: `color_map(ColorMap color)`

> This is used by the algorithm to keep track of its progress through the graph. The type `ColorMap` must be a model of Read/Write Property Map and its key type must be the graph's vertex descriptor type and the value type of the color map must model ColorValue.
> Default: an iterator_property_map created from a `std::vector` of `default_color_type` of size `num_vertices(g)` and using the `i_map` for the index map.
> Python: The color map must be a `vertex_color_map` for the graph.

IN: `vertex_index_map(VertexIndexMap i_map)`

> This maps each vertex to an integer in the range `[0, num_vertices(g))`. This parameter is only necessary when the default color property map is used. The type `VertexIndexMap` must be a model of Readable Property Map. The value type of the map must be an integer type. The vertex descriptor type of the graph needs to be usable as the key type of the map.
> Default: `get(vertex_index, g)`. Note: if you use this default, make sure your graph has an internal `vertex_index` property. For example, `adjacency_list` with `VertexList=listS` does not have an internal `vertex_index` property.
> Python: Unsupported parameter.

### Complexity

The time complexity for the connected components algorithm is also O(V + E).

### See Also

`strong_components()` and `incremental_components()`

### Example

The file `examples/connected_components.cpp` contains an example of calculating the connected components of an undirected graph.

Copyright © 2000-2001 | Jeremy Siek, Indiana University (jsiek@osl.iu.edu)