#

    adjacency_list<EdgeList, VertexList, Directed,
                   VertexProperties, EdgeProperties,
                   GraphProperties>

The `adjacency_list` class implements a generalized adjacency list graph structure. The template parameters provide many configuration options so that you can pick a version of the class that best meets your needs. An adjacency-list is basically a two-dimensional structure, where each element of the first dimension represents a vertex, and each of the vertices contains a one-dimensional structure that is its edge list. Figure 1 shows an adjacency list representation of a directed graph.

Figure 1: Adjacency List Representation of a Directed Graph.

The `VertexList` template parameter of the `adjacency_list` class controls what kind of container is used to represent the outer two-dimensional container. The `EdgeList` template parameter controls what kind of container is used to represent the edge lists. The choices for `EdgeList` and `VertexList` will determine the space complexity of the graph structure, and will determine the time complexity of the various graph operations. The possible choices and tradeoffs are discussed in Section Choosing the `Edgelist` and `VertexList`.

The `Directed` template parameter controls whether the graph is directed, undirected, or directed with access to both the in-edges and out-edges (which we call bidirectional). The bidirectional graph takes up twice the space (per edge) of a directed graph since each edge will appear in both an out-edge and in-edge list. Figure 2 shows an adjacency list representation of an undirected graph.

Figure 2: Adjacency List Representation of an Undirected Graph.

A tutorial on how to use the `adjacency_list` class is in Section Using `adjacency_list`.

### Example

A graph used to represent a family tree. The complete source code is in the file `examples/family_tree.cpp`.

      enum { Jeanie, Debbie, Rick, John, Amanda,
             Margaret, Benjamin, N };

      std::vector<std::string> name(N);
      name[Jeanie] = "Jeanie";
      name[Debbie] = "Debbie";
      name[Rick] = "Rick";
      name[John] = "John";
      name[Amanda] = "Amanda";
      name[Margaret] = "Margaret";
      name[Benjamin] = "Benjamin";

      adjacency_list<>  G(N);
      add_edge(Jeanie, Debbie, G);
      add_edge(Jeanie, Rick, G);
      add_edge(Jeanie, John, G);
      add_edge(Debbie, Amanda, G);
      add_edge(Rick, Margaret, G);
      add_edge(John, Benjamin, G);

      graph_traits< adjacency_list<> >::vertex_iterator i, end;
      graph_traits< adjacency_list<> >::adjacency_iterator ai, a_end;

      property_map<adjacency_list<>, vertex_index_t>::type
        id = get(vertex_index, G);

      for(tie(i,end) = vertices(G); i != end; ++i) {
        cout << name[get(id, *i)];
        tie(ai, a_end) = adjacent_vertices(*i, G);
        if (ai == a_end)
          cout << " has no children";
        else
          cout << " is the parent of ";
        for (; ai != a_end; ++ai)
          cout << name[get(id, *ai)] << "  ";
        cout << endl;
      }

The output is:

      Jeanie is the parent of Debbie  Rick  John
      Debbie is the parent of Amanda
      Rick is the parent of Margaret
      John is the parent of Benjamin
      Amanda has no children
      Margaret has no children
      Benjamin has no children

### Template Parameters

Parameter | Description | Default
--- | --- | ---
`EdgeList` | The selector for the container used to represent the edge-list for each of the vertices. | `vecS`
`VertexList` | The selector for the container used to represent the vertex-list of the graph. | `vecS`
`Directed` | A selector to choose whether the graph is directed, undirected, or directed with bidirectional edge access (access to both out-edges and in-edges). The options are `directedS`, `undirectedS`, and `bidirectionalS`. | `directedS`
`VertexProperties` | for specifying internal property storage. | `no_property`
`EdgeProperties` | for specifying internal property storage. | `no_property`
`GraphProperties` | for specifying property storage for the graph object. | `no_property`

### Model of

VertexAndEdgeListGraph, MutablePropertyGraph

### Where Defined

`boost/graph/adjacency_list.hpp`

## Vertex and Edge Properties

Properties such as color, distance, weight, and user-defined properties can be attached to the vertices and edges of the graph using properties. The property values can be read from and written to via the property maps provided by the graph. The property maps are obtained via the `get(property, g)` function. How to use properties is described in Section Internal Properties . The property maps are objects that implement the interface defined in Section Property Map Concepts. The property maps obtained from a const `adjacency_list` graph object are models of the ReadablePropertyMap concept. The property maps obtained from a mutable graph object are models of the ReadWritePropertyMap concept.

If the `VertexList` of the graph is `vecS`, then the graph has a builtin vertex indices accessed via the property map for the `vertex_index_t` property. The indices fall in the range `[0, num_vertices(g))` and are contiguous. When a vertex is removed the indices are adjusted so that they retain these properties. Some care must be taken when using these indices to access exterior property storage.

## Iterator and Descriptor Stability/Invalidation

Some care must be taken when changing the structure of a graph (via adding or removing edges). Depending on the type of `adjacency_list` and on the operation, some of the iterator or descriptor objects that point into the graph may become invalid. For example, the following code will result in undefined (bad) behavior:

      typedef adjacency_list<listS, vecS> Graph; // VertexList=vecS
      Graph G(N);
      // Fill in the graph...

      // Attempt to remove all the vertices. Wrong!
      graph_traits<Graph>::vertex_iterator vi, vi_end;
      for (tie(vi, vi_end) = vertices(G); vi != vi_end; ++vi)
        remove_vertex(*vi, G);

      // Remove all the vertices. This is still wrong!
      graph_traits<Graph>::vertex_iterator vi, vi_end, next;
      tie(vi, vi_end) = vertices(G);
      for (next = vi; vi != vi_end; vi = next) {
        ++next;
        remove_vertex(*vi, G);
      }

The reason this is a problem is that we are invoking `remove_vertex()`, which when used with an `adjacency_list` where `VertexList=vecS`, invalidates all iterators and descriptors for the graph (such as `vi` and `vi_end`), thereby causing trouble in subsequent iterations of the loop.

If we use a different kind of `adjacency_list`, where `VertexList=listS`, then the iterators are not invalidated by calling `remove_vertex` unless the iterator is pointing to the actual vertex that was removed. The following code demonstrates this.

      typedef adjacency_list<listS, listS> Graph; // VertexList=listS
      Graph G(N);
      // Fill in the graph...

      // Attempt to remove all the vertices. Wrong!
      graph_traits<Graph>::vertex_iterator vi, vi_end;
      for (tie(vi, vi_end) = vertices(G); vi != vi_end; ++vi)
        remove_vertex(*vi, G);

      // Remove all the vertices. This is OK.
      graph_traits<Graph>::vertex_iterator vi, vi_end, next;
      tie(vi, vi_end) = vertices(G);
      for (next = vi; vi != vi_end; vi = next) {
        ++next;
        remove_vertex(*vi, G);
      }

The stability issue also affects vertex and edge descriptors. For example, suppose you use vector of vertex descriptors to keep track of the parents (or predecessors) of vertices in a shortest paths tree (see `examples/dijkstra.cpp`). You create the parent vector with a call to `dijkstra_shortest_paths()`, and then remove a vertex from the graph. Subsequently you try to use the parent vector, but since all vertex descriptors have become invalid, the result is incorrect.

      std::vector<Vertex> parent(num_vertices(G));
      std::vector<Vertex> distance(num_vertices(G));

      dijkstra_shortest_paths(G, s, &distance[0],
        make_ucs_visitor(record_predecessors(&parent[0], on_edge_relaxed())));

      remove_vertex(s, G); // Bad idea! Invalidates vertex descriptors in parent vector.

      // The following will produce incorrect results
      for(tie(vi, vend) = vertices(G); vi != vend; ++vi)
        std::cout << p[*vi] << " is the parent of " << *vi << std::endl;

Note that in this discussion iterator and descriptor invalidation is concerned with the invalidation of iterators and descriptors that are not directly affected by the operation. For example, performing `remove_edge(u, v, g)` will always invalidate any edge descriptor for (u,v) or edge iterator pointing to (u,v), regardless of the kind `adjacency_list`. In this discussion of iterator and descriptor invalidation, we are only concerned with the affect of `remove_edge(u, v, g)` on edge descriptors and iterators that point to other edges (not (u,v)).

In general, if you want your vertex and edge descriptors to be stable (never invalidated) then use `listS` or `setS` for the `VertexList` and `EdgeList` template parameters of `adjacency_list`. If you are not as concerned about descriptor and iterator stability, and are more concerned about memory consumption and graph traversal speed, use `vecS` for the `VertexList` and/or `EdgeList` template parameters.

The following table summarizes which operations cause descriptors and iterators to become invalid. In the table, `EL` is an abbreviation for `EdgeList` and `VL` means `VertexList`. The Adj Iter category includes the `out_edge_iterator`, `in_edge_iterator`, and `adjacency_iterator` types. A more detailed description of descriptor and iterator invalidation is given in the documentation for each operation.

Table: Summary of Descriptor and Iterator Invalidation.
Function | Vertex Desc | Edge Desc | Vertex Iter | Edge Iter | Adj Iter
--- | --- | --- | --- | --- | ---
`add_edge()` | `OK` | `OK` | `OK` | `EL=vecS && Directed=directedS` | `EL=vecS`
`remove_edge() remove_edge_if() remove_out_edge_if() remove_in_edge_if() clear_vertex()` | `OK` | `OK` | `OK` | `EL=vecS && Directed=directedS` | `EL=vecS`
`add_vertex()` | `OK` | `OK` | `OK` | `OK` | `OK`
`remove_vertex()` | `VL=vecS` | `VL=vecS` | `VL=vecS` | `VL=vecS` | `VL=vecS`

## Associated Types

`graph_traits<adjacency_list>::vertex_descriptor`
and
`adjacency_list_traits<EdgeList, VertexList, Directed>::vertex_descriptor`
The type for the vertex descriptors associated with the `adjacency_list`.

`graph_traits<adjacency_list>::edge_descriptor`
and
`adjacency_list_traits<EdgeList, VertexList, Directed>::edge_descriptor`
The type for the edge descriptors associated with the `adjacency_list`.

`graph_traits<adjacency_list>::vertex_iterator`
The type for the iterators returned by `vertices()`. When `VertexList=vecS` then the `vertex_iterator` models RandomAccessIterator. Otherwise the `vertex_iterator` models BidirectionalIterator.

`graph_traits<adjacency_list>::edge_iterator`
The type for the iterators returned by `edges()`. The `edge_iterator` models BidirectionalIterator.

`graph_traits<adjacency_list>::out_edge_iterator`
The type for the iterators returned by `out_edges()`. When `EdgeList=vecS` then the `out_edge_iterator` models RandomAccessIterator. When `EdgeList=slistS` then the `out_edge_iterator` models ForwardIterator. Otherwise the `out_edge_iterator` models BidirectionalIterator.

`graph_traits<adjacency_list>::adjacency_iterator`
The type for the iterators returned by `adjacent_vertices()`. The `adjacency_iterator` models the same iterator concept as `out_edge_iterator`.

`graph_traits<adjacency_list>::directed_category`
and
`adjacency_list_traits<EdgeList, VertexList, Directed>::directed_category`
Provides information about whether the graph is directed (`directed_tag`) or undirected (`undirected_tag`).

`graph_traits<adjacency_list>::edge_parallel_category`
and
`adjacency_list_traits<EdgeList, VertexList, Directed>::edge_parallel_category`
This describes whether the graph class allows the insertion of parallel edges (edges with the same source and target). The two tags are `allow_parallel_edge-_tag` and `disallow_parallel_edge_tag`. The `setS` and `hash_setS` variants disallow parallel edges while the others allow parallel edges.

`graph_traits<adjacency_list>::vertices_size_type`
The type used for dealing with the number of vertices in the graph.

`graph_traits<adjacency_list>::edge_size_type`
The type used for dealing with the number of edges in the graph.

`graph_traits<adjacency_list>::degree_size_type`
The type used for dealing with the number of edges incident to a vertex in the graph.

`property_map<adjacency_list, Property>::type`
and
`property_map<adjacency_list, Property>::const_type`
The property map type for vertex or edge properties in the graph. The specific property is specified by the `Property` template argument, and must match one of the properties specified in the `VertexProperties` or `EdgeProperties` for the graph.

`graph_property<adjacency_list, Property>::type`
The property value type for the graph property specified by the `Property` tag.

## Member Functions

    adjacency_list(const GraphProperty& p = GraphProperty())

Default constructor. Creates an empty graph object with zero vertices and zero edges.

    adjacency_list(const adjacency_list& x)

Copy constructor. Creates a new graph that is a copy of graph `x`, including the edges, vertices, and properties.

    adjacency_list& operator=(const adjacency_list& x)

Assignment operator. Makes this graph a copy of graph `x`, including the edges, vertices, and properties.

    adjacency_list(vertices_size_type n,
                   const GraphProperty& p = GraphProperty())

Creates a graph object with `n` vertices and zero edges.

    template <class EdgeIterator>
    adjacency_list(vertices_size_type n,
                   EdgeIterator first, EdgeIterator last,
                   const GraphProperty& p = GraphProperty())

Creates a graph object with `n` vertices and with the edges specified in the edge list given by the range `[first, last)`. The `EdgeIterator` must be a model of InputIterator. The value type of the `EdgeIterator` must be a `std::pair`, where the type in the pair is an integer type. The integers will correspond to vertices, and they must all fall in the range of `[0, n)`.

    template <class EdgeIterator, class EdgePropertyIterator>
    adjacency_list(vertices_size_type num_vertices,
                   EdgeIterator first, EdgeIterator last,
                   EdgePropertyIterator ep_iter,
                   const GraphProperty& p = GraphProperty())

Creates a graph object with `n` vertices and with the edges specified in the edge list given by the range `[first, last)`. The `EdgeIterator` and `EdgePropertyIterator` must be a model of InputIterator. The value type of the `EdgeIterator` must be a `std::pair`, where the type in the pair is an integer type. The integers will correspond to vertices, and they must all fall in the range of `[0, n)`. The `value_type` of the `ep_iter` should be `EdgeProperties`.

    void clear()

Remove all of the edges and vertices from the graph.

    void swap(adjacency_list& x)

Swap the vertices, edges, and properties of this graph with the vertices, edges, and properties of graph `x`.

## Non-Member Functions

#### Structure Access

    std::pair<vertex_iterator, vertex_iterator>
    vertices(const adjacency_list& g)

Returns an iterator-range providing access to the vertex set of graph `g`.

    std::pair<edge_iterator, edge_iterator>
    edges(const adjacency_list& g)

Returns an iterator-range providing access to the edge set of graph `g`.

    std::pair<adjacency_iterator, adjacency_iterator>
    adjacent_vertices(vertex_descriptor u, const adjacency_list& g)

Returns an iterator-range providing access to the vertices adjacent to vertex `u` in graph `g`.

    std::pair<out_edge_iterator, out_edge_iterator>
    out_edges(vertex_descriptor u, const adjacency_list& g)

Returns an iterator-range providing access to the out-edges of vertex `u` in graph `g`. If the graph is undirected, this iterator-range provides access to all edges incident on vertex `u`. For both directed and undirected graphs, for an out-edge `e`, `source(e, g) == u` and `target(e, g) == v` where `v` is a vertex adjacent to `u`.

    std::pair<in_edge_iterator, in_edge_iterator>
    in_edges(vertex_descriptor v, const adjacency_list& g)

Returns an iterator-range providing access to the in-edges of vertex `v` in graph `g`. This operation is only available if `bidirectionalS` was specified for the `Directed` template parameter. For an in-edge `e`, `target(e, g) == v` and `source(e, g) == u` for some vertex `u` that is adjacent to `v`, whether the graph is directed or undirected.

    vertex_descriptor
    source(edge_descriptor e, const adjacency_list& g)

Returns the source vertex of edge `e`.

    vertex_descriptor
    target(edge_descriptor e, const adjacency_list& g)

Returns the target vertex of edge `e`.

    degree_size_type
    out_degree(vertex_descriptor u, const adjacency_list& g)

Returns the number of edges leaving vertex `u`.

    degree_size_type
    in_degree(vertex_descriptor u, const adjacency_list& g)

Returns the number of edges entering vertex `u`. This operation is only available if `bidirectionalS` was specified for the `Directed` template parameter.

    vertices_size_type
    num_vertices(const adjacency_list& g)

Returns the number of vertices in the graph `g`.

    edges_size_type
    num_edges(const adjacency_list& g)

Returns the number of edges in the graph `g`.

    vertex_descriptor
    vertex(vertices_size_type n, const adjacency_list& g)

Returns the nth vertex in the graph's vertex list.

    std::pair<edge_descriptor, bool>
    edge(vertex_descriptor u, vertex_descriptor v,
         const adjacency_list& g)

Returns the edge connecting vertex `u` to vertex `v` in graph `g`.

    std::pair<out_edge_iterator, out_edge_iterator>
    edge_range(vertex_descriptor u, vertex_descriptor v,
               const adjacency_list& g)

Returns a pair of out-edge iterators that give the range for all the parallel edges from `u` to `v`. This function only works when the `EdgeList` for the `adjacency_list` is a container that sorts the out edges according to target vertex, and allows for parallel edges. The `multisetS` selector chooses such a container.

#### Structure Modification

    std::pair<edge_descriptor, bool>
    add_edge(vertex_descriptor u, vertex_descriptor v,
             adjacency_list& g)

Adds edge (u,v) to the graph and returns the edge descriptor for the new edge. For graphs that do not allow parallel edges, if the edge is already in the graph then a duplicate will not be added and the `bool` flag will be `false`. Also, if u and v are descriptors for the same vertex (creating a self loop) and the graph is undirected, then the edge will not be added and the flag will be `false`. When the flag is `false`, the returned edge descriptor points to the already existing edge.

The placement of the new edge in the out-edge list is in general unspecified, though ordering of the out-edge list can be accomplished through the choice of `EdgeList`. If the `VertexList` selector is `vecS`, and if either vertex descriptor `u` or `v` (which are integers) has a value greater than the current number of vertices in the graph, the graph is enlarged so that the number of vertices is `std::max(u,v) + 1`.

If the `EdgeList` selector is `vecS` then this operation will invalidate any `out_edge_iterator` for vertex u. This also applies if the `EdgeList` is a user-defined container that invalidates its iterators when `push(container, x)` is invoked (see Section Customizing the Adjacency List Storage). If the graph is also bidirectional then any `in_edge_iterator` for v is also invalidated. If instead the graph is undirected then any `out_edge_iterator` for v is also invalidated. If instead the graph is directed, then `add_edge()` also invalidates any `edge_iterator`.

    std::pair<edge_descriptor, bool>
    add_edge(vertex_descriptor u, vertex_descriptor v,
             const EdgeProperties& p,
             adjacency_list& g)

Adds edge (u,v) to the graph and attaches `p` as the value of the edge's internal property storage. Also see the previous `add_edge()` member function for more details.

    void remove_edge(vertex_descriptor u, vertex_descriptor v,
                     adjacency_list& g)

Removes the edge (u,v) from the graph.

This operation causes any outstanding edge descriptors or iterators that point to edge (u,v) to become invalid. In addition, if the `EdgeList` selector is `vecS` then this operation will invalidate any iterators that point into the edge-list for vertex u and also for vertex v in the undirected and bidirectional case. Also, for directed graphs this invalidates any `edge_iterator`.

    void remove_edge(edge_descriptor e, adjacency_list& g)

Removes the edge `e` from the graph. This differs from the `remove_edge(u, v, g)` function in the case of a multigraph. This `remove_edge(e, g)` function removes a single edge, whereas the `remove_edge(u, v, g)` function removes all edges (u,v).

This operation invalidates any outstanding edge descriptors and iterators for the same edge pointed to by descriptor `e`. In addition, this operation will invalidate any iterators that point into the edge-list for the `target(e, g)`. Also, for directed graphs this invalidates any `edge_iterator` for the graph.

    void remove_edge(out_edge_iterator iter, adjacency_list& g)

This has the same effect as `remove_edge(*iter, g)`. The difference is that this function has constant time complexity in the case of directed graphs, whereas `remove_edge(e, g)` has time complexity O(E/V).

    template <class Predicate>
    void remove_out_edge_if(vertex_descriptor u, Predicate predicate,
                            adjacency_list& g)

Removes all out-edges of vertex u from the graph that satisfy the `predicate`. That is, if the predicate returns true when applied to an edge descriptor, then the edge is removed.

The affect on descriptor and iterator stability is the same as that of invoking `remove_edge()` on each of the removed edges.

    template <class Predicate>
    void remove_in_edge_if(vertex_descriptor v, Predicate predicate,
                           adjacency_list& g)

Removes all in-edges of vertex v from the graph that satisfy the `predicate`. That is, if the predicate returns true when applied to an edge descriptor, then the edge is removed.

The affect on descriptor and iterator stability is the same as that of invoking `remove_edge()` on each of the removed edges.

This operation is available for undirected and bidirectional `adjacency_list` graphs, but not for directed.

    template <class Predicate>
    void remove_edge_if(Predicate predicate, adjacency_list& g)

Removes all edges from the graph that satisfy the `predicate`. That is, if the predicate returns true when applied to an edge descriptor, then the edge is removed.

The affect on descriptor and iterator stability is the same as that of invoking `remove_edge()` on each of the removed edges.

    vertex_descriptor
    add_vertex(adjacency_list& g)

Adds a vertex to the graph and returns the vertex descriptor for the new vertex.

    vertex_descriptor
    add_vertex(const VertexProperties& p,
               adjacency_list& g)

Adds a vertex to the graph with the specified properties. Returns the vertex descriptor for the new vertex.

    void clear_vertex(vertex_descriptor u, adjacency_list& g)

Removes all edges to and from vertex u. The vertex still appears in the vertex set of the graph.

The affect on descriptor and iterator stability is the same as that of invoking `remove_edge()` for all of the edges that have `u` as the source or target.

    void remove_vertex(vertex_descriptor u, adjacency_list& g)

Remove vertex u from the vertex set of the graph. It is assumed that there are no edges to or from vertex u when it is removed. One way to make sure of this is to invoke `clear_vertex()` beforehand.

If the `VertexList` template parameter of the `adjacency_list` was `vecS`, then all vertex descriptors, edge descriptors, and iterators for the graph are invalidated by this operation. The builtin `vertex_index_t` property for each vertex is renumbered so that after the operation the vertex indices still form a contiguous range `[0, num_vertices(g))`. If you are using external property storage based on the builtin vertex index, then the external storage will need to be adjusted. Another option is to not use the builtin vertex index, and instead use a property to add your own vertex index property. If you need to make frequent use of the `remove_vertex()` function the `listS` selector is a much better choice for the `VertexList` template parameter.

#### Property Map Access

    template <class Property>
    property_map<adjacency_list, Property>::type
    get(Property, adjacency_list& g)

    template <class Property>
    property_map<adjacency_list, Tag>::const_type
    get(Property, const adjacency_list& g)

Returns the property map object for the vertex property specified by `Property`. The `Property` must match one of the properties specified in the graph's `VertexProperty` template argument.

    template <class Property, class X>
    typename property_traits<property_map<adjacency_list, Property>::const_type>::value_type
    get(Property, const adjacency_list& g, X x)

This returns the property value for `x`, where `x` is either a vertex or edge descriptor.

    template <class Property, class X, class Value>
    void
    put(Property, const adjacency_list& g, X x, const Value& value)

This sets the property value for `x` to `value`. `x` is either a vertex or edge descriptor. `Value` must be convertible to `typename property_traits<property_map<adjacency_list, Property>::type>::value_type`

    template <class GraphProperties, class GraphProperty>
    typename graph_property<adjacency_list, GraphProperty>::type&
    get_property(adjacency_list& g, GraphProperty);

Return the property specified by `GraphProperty` that is attached to the graph object `g`. The `graph_property` traits class is defined in `boost/graph/adjacency_list.hpp`.

    template <class GraphProperties, class GraphProperty>
    const typename graph_property<adjacency_list, GraphProperty>::type&
    get_property(const adjacency_list& g, GraphProperty);

Return the property specified by `GraphProperty` that is attached to the graph object `g`. The `graph_property` traits class is defined in `boost/graph/adjacency_list.hpp`.

### See Also

`adjacency_list_traits`, `property_map`, `graph_traits`

Copyright © 2000 | Jeremy Siek, Univ.of Notre Dame (jsiek@lsc.nd.edu) Lie-Quan Lee, Univ.of Notre Dame (llee1@lsc.nd.edu) Andrew Lumsdaine, Univ.of Notre Dame (lums@lsc.nd.edu)