# `strong_components`

    template <class Graph, class ComponentMap, class P, class T, class R>
    typename property_traits<ComponentMap>::value_type
    strong_components(Graph& g, ComponentMap comp,
        const bgl_named_params<P, T, R>& params = all defaults)

The `strong_components()` functions compute the strongly connected components of a directed graph using Tarjan's algorithm based on DFS [41].

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

### Where Defined

`boost/graph/strong_components.hpp`

### Definitions

A strongly connected component of a directed graph G=(V,E) is a maximal set of vertices U which is in V such that for every pair of vertices u and v in U, we have both a path from u to v and path from v to u. That is to say that u and v are reachable from each other.

### Parameters

IN: `const Graph& g`

> A directed graph. The graph type must be a model of Vertex List Graph and Incidence 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 shouch 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.

### Named Parameters

UTIL: `root_map(RootMap r_map)`

> This is used by the algorithm to record the candidate root vertex for each vertex. By the end of the algorithm, there is a single root vertex for each component and `get(r_map, v)` returns the root vertex for whichever component vertex `v` is a member. The `RootMap` must be a Read/Write Property Map, where the key type and the value type are the vertex descriptor type of the graph.
> Default: an `iterator_property_map` created from a `std::vector` of vertex descriptors of size `num_vertices(g)` and using the `i_map` for the index map.

UTIL: `discover_time(TimeMap t_map)`

> This is used by the algorithm to keep track of the DFS ordering of the vertices. The `TimeMap` must be a model of Read/Write Property Map and its value type must be an integer type. The key type must be the vertex descriptor type of the graph.
> Default:an `iterator_property_map` created from a `std::vector` of integers with size `num_vertices(g)` and using the `i_map` for the index map.

UTIL: `color_map(ColorMap c_map)`

> 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.

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 a default is used for one of the other named parameters. 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)`

### Complexity

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

### See Also

`connected_components()` and `incremental_components()`

### Example

See `examples/strong_components.cpp`.

Copyright © 2000 | Jeremy Siek, Univ.of Notre Dame (jsiek@lsc.nd.edu)