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<Head>
<Title>Boost Graph Library: Adjacency List</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
        ALINK="#ff0000">
<IMG SRC="../../../boost.png"
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<BR Clear>

<H1><A NAME="sec:adjacency-list-class"></A>
<pre>
adjacency_list&lt;OutEdgeList, VertexList, Directed,
               VertexProperties, EdgeProperties,
               GraphProperties, EdgeList&gt;
</pre>
</H1>


<P>
The <TT>adjacency_list</TT> 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 <a
href="graph_theory_review.html#sec:adjacency-list-representation">adjacency-list</a>
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. <a
href="#fig:adj-list-graph">Figure 1</a> shows an adjacency list
representation of a directed graph.

<P></P>
<DIV ALIGN="center"><A NAME="fig:adj-list-graph"></A>
<TABLE>
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 1:</STRONG> Adjacency List Representation of a Directed Graph.</CAPTION>
<TR><TD><IMG SRC="./figs/adj-matrix-graph2.gif" width="386" height="284"></TD>
<TD><IMG SRC="./figs/adj-list2.gif" width="62" height="122"></TD></TR>
</TABLE>
</DIV><P></P>

The
<TT>VertexList</TT> template parameter of the <TT>adjacency_list</TT>
class controls what kind of container is used to represent the outer
two-dimensional container. The <TT>OutEdgeList</TT> template parameter
controls what kind of container is used to represent the edge
lists. The choices for <TT>OutEdgeList</TT> and <TT>VertexList</TT> 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 <A
HREF="./using_adjacency_list.html#sec:choosing-graph-type">Choosing
the <TT>Edgelist</TT> and <TT>VertexList</TT></A>.

<P>
The <TT>Directed</TT> 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. <a
href="#fig:undir-adj-list-graph">Figure 2</a> shows an adjacency list
representation of an undirected graph.

<P></P>
<DIV ALIGN="center"><A NAME="fig:undir-adj-list-graph"></A>
<TABLE>
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 2:</STRONG> Adjacency List Representation of an Undirected Graph.</CAPTION>
<TR><TD><IMG SRC="./figs/undir-adj-matrix-graph2.gif" width="260" height="240"></TD>
<TD><IMG SRC="./figs/undir-adj-list.gif" width="62" height="122"></TD></TR>
</TABLE>
</DIV><P></P>

<P>
A tutorial on how to use the <TT>adjacency_list</TT> class is in
Section <A HREF="./using_adjacency_list.html">Using
<TT>adjacency_list</TT></A>.

<P>

<H3>Example</H3>

<P>
The example in <a
href="../example/family-tree-eg.cpp"><tt>examples/family-tree-eg.cpp</tt></a>
shows how to represent a family tree with a graph.

<H3>Template Parameters</H3>

<P>
<TABLE border>
<TR>
<th>Parameter</th><th>Description</th><th>Default</th>
</tr>

<TR><TD><TT>OutEdgeList</TT></TD>
<TD>The selector for the container used to represent the
  edge-list for each of the vertices.</TD>
<TD><TT>vecS</TT></TD>
</TR>

<TR>
<TD><TT>VertexList</TT></TD>
<TD>The selector for the container used to represent the
  vertex-list of the graph.</TD>
<TD><TT>vecS</TT></TD>
</TR>

<TR>
<TD><TT>Directed</TT></TD>
<TD>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 <TT>directedS</TT>, <TT>undirectedS</TT>, and <TT>bidirectionalS</TT>.</TD>
<TD><TT>directedS</TT></TD>
</TR>

<TR>
<TD><TT>VertexProperties</TT></TD>
<TD>for specifying internal property storage.</TD>
<TD><TT>no_property</TT></TD>
</TR>

<TR>
<TD><TT>EdgeProperties</TT></TD>
<TD>for specifying internal property storage.</TD>
<TD><TT>no_property</TT></TD>
</TR>

<TR>
<TD><TT>GraphProperties</TT></TD>
<TD>for specifying property storage for the graph object.</TD>
<TD><TT>no_property</TT></TD>
</TR>

<TR><TD><TT>EdgeList</TT></TD>
<TD>The selector for the container used to represent the
  edge-list for the graph.</TD>
<TD><TT>listS</TT></TD>
</TR>

</TABLE>
<P>

<H3>Model of</H3>

<P>
<a href="./VertexAndEdgeListGraph.html">VertexAndEdgeListGraph</a>,
<a href="./MutablePropertyGraph.html">MutablePropertyGraph</a>,
<a href="../../utility/CopyConstructible.html">CopyConstructible</a>,
<a href="../../utility/Assignable.html">Assignable</a>,
and <a href="../../serialization/doc/index.html">Serializable</a>.


<P>

<H3>Where Defined</H3>

<P>
<a href="../../../boost/graph/adjacency_list.hpp"><TT>boost/graph/adjacency_list.hpp</TT></a><br><br>
Also, the serialization functionality is in
<a href="../../../boost/graph/adj_list_serialize.hpp"><tt>boost/graph/adj_list_serialize.hpp</tt></a>.
<P>

<H2>Vertex and Edge Properties</H2>

<P>
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 <TT>get(property, g)</TT> function.  How to use
properties is described in Section <A
HREF="./using_adjacency_list.html#sec:adjacency-list-properties">Internal
Properties </A>. The property maps are objects that implement the
interface defined in Section <A
HREF="../../property_map/doc/property_map.html">Property Map
Concepts</A> or may be <a href="bundles.html">bundled properties</a>,
which have a more succinct syntax. The types of all property values
must be Copy Constructible, Assignable, and Default Constructible.
The property maps obtained from the
<TT>adjacency_list</TT> class are models of the <a
href="../../property_map/doc/LvaluePropertyMap.html">Lvalue Property
Map</a> concept. If the <TT>adjacency_list</TT> is const,
then the property map is constant, otherwise the property
map is mutable.

<P>
If the <TT>VertexList</TT> of the graph is <TT>vecS</TT>, then the
graph has a builtin vertex indices accessed via the property map for
the <TT>vertex_index_t</TT> property.  The indices fall in the range
<TT>[0, num_vertices(g))</TT> 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. The property map for vertex index is a
model of <a href="../../property_map/doc/ReadablePropertyMap.html">Readable
Property Map</a>.

<P>

<h2>Iterator and Descriptor Stability/Invalidation</h2>

Some care must be taken when changing the structure of a graph (via
adding or removing edges). Depending on the type of
<tt>adjacency_list</tt> 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:

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

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

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

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

<p>

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

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

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

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

<p>

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 <a
href="../example/dijkstra-example.cpp"><tt>examples/dijkstra-example.cpp</tt></a>).
You create the parent vector with a call to
<tt>dijkstra_shortest_paths()</tt>, 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.

<pre>
  std::vector&lt;Vertex&gt; parent(num_vertices(G));
  std::vector&lt;Vertex&gt; distance(num_vertices(G));

  dijkstra_shortest_paths(G, s, distance_map(&amp;distance[0]).
    predecessor_map(&amp;parent[0]));

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

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


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

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

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

<p>

<table border>
<CAPTION ALIGN="BOTTOM"><STRONG>Table:</STRONG>
    Summary of Descriptor and Iterator Invalidation.
    </CAPTION>
<tr>
    <th>Function</th>
    <th>Vertex Desc</th>
    <th>Edge Desc</th>
    <th>Vertex Iter</th>
    <th>Edge Iter</th>
    <th>Adj Iter</th>
</tr>
<tr>
<td>
    <tt>add_edge()</tt></td>
    <td align=center><tt>OK</tt></td>
    <td align=center><tt>OK</tt></td>
    <td align=center><tt>OK</tt></td>
    <td align=center><tt>EL=vecS &amp;&amp; <br>Directed=directedS</tt></td>
    <td align=center><tt>EL=vecS</tt></td>
</tr>
<tr>
    <td><tt>remove_edge()<br>remove_edge_if()<br>remove_out_edge_if()<br>
            remove_in_edge_if()<br>clear_vertex()</tt>
    </td>
    <td align=center><tt>OK</tt></td>
    <td align=center><tt>OK</tt></td>
    <td align=center><tt>OK</tt></td>
    <td align=center><tt>EL=vecS &amp;&amp; <br>Directed=directedS</tt></td>
    <td align=center><tt>EL=vecS</tt></td>
</tr>
<tr>
    <td><tt>add_vertex()</tt></td>
    <td align=center><tt>OK</tt></td>
    <td align=center><tt>OK</tt></td>
    <td align=center><tt>OK</tt></td>
    <td align=center><tt>VL=vecS &amp;&amp; <br/> Directed=directedS</tt></td>
    <td align=center><tt>VL=vecS &amp;&amp; <br/> Directed=directedS</tt></td>
</tr>
<tr>
    <td><tt>remove_vertex()</tt></td>
    <td align=center><tt>VL=vecS</tt></td>
    <td align=center><tt>VL=vecS</tt></td>
    <td align=center><tt>VL=vecS</tt></td>
    <td align=center><tt>VL=vecS</tt></td>
    <td align=center><tt>VL=vecS</tt></td>
</tr>
</table>

<H2>Associated Types</H2>

<hr>

<tt>graph_traits&lt;adjacency_list&gt;::vertex_descriptor</tt>
<br>
and
<br>
<tt>adjacency_list_traits&lt;OutEdgeList, VertexList, Directed, EdgeList&gt;::vertex_descriptor</tt>
<br><br>
The type for the vertex descriptors associated with the
<TT>adjacency_list</TT>.

<hr>

<tt>graph_traits&lt;adjacency_list&gt;::edge_descriptor</tt><br>
and<br>
<tt>adjacency_list_traits&lt;OutEdgeList, VertexList, Directed, EdgeList&gt;::edge_descriptor</tt>
<br><br>
The type for the edge descriptors associated with the
<TT>adjacency_list</TT>.

<hr>

<tt>graph_traits&lt;adjacency_list&gt;::vertex_iterator</tt>
<br><br>
The type for the iterators returned by <TT>vertices()</TT>.

When <tt>VertexList=vecS</tt> then the <tt>vertex_iterator</tt> models
<a
href="http://www.boost.org/sgi/stl/RandomAccessIterator.html">RandomAccessIterator</a>. Otherwise
the <tt>vertex_iterator</tt> models <a
href="http://www.boost.org/sgi/stl/BidirectionalIterator.html">BidirectionalIterator</a>.

<hr>

<tt>graph_traits&lt;adjacency_list&gt;::edge_iterator</tt>
<br><br>
The type for the iterators returned by <TT>edges()</TT>.
The <tt>edge_iterator</tt> models <a
href="http://www.boost.org/sgi/stl/BidirectionalIterator.html">BidirectionalIterator</a>.


<hr>


<tt>graph_traits&lt;adjacency_list&gt;::out_edge_iterator</tt>
<br><br>

The type for the iterators returned by <TT>out_edges()</TT>.
When <tt>OutEdgeList=vecS</tt> then the <tt>out_edge_iterator</tt> models
<a href="http://www.boost.org/sgi/stl/RandomAccessIterator.html">
RandomAccessIterator</a>.  When <tt>OutEdgeList=slistS</tt> then the
<tt>out_edge_iterator</tt> models <a
href="http://www.boost.org/sgi/stl/ForwardIterator.html">
ForwardIterator</a>.  Otherwise the <tt>out_edge_iterator</tt> models
<a
href="http://www.boost.org/sgi/stl/BidirectionalIterator.html">
BidirectionalIterator</a>.

<hr>

<tt>graph_traits&lt;adjacency_list&gt;::adjacency_iterator</tt>
<br><br>
The type for the iterators returned by <TT>adjacent_vertices()</TT>.
The <tt>adjacency_iterator</tt> models the same iterator concept
as <tt>out_edge_iterator</tt>.
<hr>

<tt>adjacency_list::inv_adjacency_iterator</tt>
<br><br>
The type for the iterators returned by <TT>inv_adjacent_vertices()</TT>.
The <tt>inv_adjacency_iterator</tt> models the same iterator concept
as <tt>out_edge_iterator</tt>.
<hr>

<tt>graph_traits&lt;adjacency_list&gt;::directed_category</tt><br>
and<br>
<tt>adjacency_list_traits&lt;OutEdgeList, VertexList, Directed, EdgeList&gt;::directed_category</tt>
<br><br>
Provides information about whether the graph is
directed (<TT>directed_tag</TT>) or undirected
(<TT>undirected_tag</TT>).

<hr>

<tt>graph_traits&lt;adjacency_list&gt;::edge_parallel_category</tt><br>
and<br>
<tt>adjacency_list_traits&lt;OutEdgeList, VertexList, Directed, EdgeList&gt;::edge_parallel_category</tt>
<br><br>
This describes whether the graph class allows the insertion of
parallel edges (edges with the same source and target). The two tags
are <TT>allow_parallel_edge_tag</TT> and
<TT>disallow_parallel_edge_tag</TT>. The
<TT>setS</TT> and <TT>hash_setS</TT> variants disallow
parallel edges while the others allow parallel edges.

<hr>

<tt>graph_traits&lt;adjacency_list&gt;::vertices_size_type</tt><br>
and<br>
<tt>adjacency_list_traits&lt;OutEdgeList, VertexList, Directed_list, EdgeList&gt;::vertices_size_type</tt><br>
<br><br>
The type used for dealing with the number of vertices in the graph.

<hr>

<tt>graph_traits&lt;adjacency_list&gt;::edges_size_type</tt><br>
and<br>
<tt>adjacency_list_traits&lt;OutEdgeList, VertexList, Directed_list, EdgeList&gt;::edges_size_type</tt><br>
<br><br>
The type used for dealing with the number of edges in the graph.

<hr>

<tt>graph_traits&lt;adjacency_list&gt;::degree_size_type</tt>
<br><br>
The type used for dealing with the number of edges incident to a vertex
in the graph.

<hr>

<tt>property_map&lt;adjacency_list, Property&gt;::type</tt><br>
and<br>
<tt>property_map&lt;adjacency_list, Property&gt;::const_type</tt>
<br><br>
The property map type for vertex or edge properties in the graph. The
specific property is specified by the <TT>Property</TT> template argument,
and must match one of the properties specified in the
<TT>VertexProperties</TT> or <TT>EdgeProperties</TT> for the graph.

<hr>

<tt>graph_property&lt;adjacency_list, Property&gt;::type</tt>
<br><br>
The property value type for the graph property specified by the
<tt>Property</tt> tag.

<hr>

<tt>adjacency_list::out_edge_list_selector</tt>
<br><br>
The type <tt>OutEdgeListS</tt>.

<hr>

<tt>adjacency_list::vertex_list_selector</tt>
<br><br>
The type <tt>VertexListS</tt>.

<hr>

<tt>adjacency_list::directed_selector</tt>
<br><br>
The type <tt>DirectedS</tt>.

<hr>

<tt>adjacency_list::edge_list_selector</tt>
<br><br>
The type <tt>EdgeListS</tt>.

<hr>

<H2>Member Functions</H2>

<hr>

<pre>
adjacency_list(const&nbsp;GraphProperty&amp;&nbsp;p = GraphProperty())
</pre>
Default constructor. Creates an empty graph object with zero vertices
and zero edges.

<hr>

<pre>
adjacency_list(const&nbsp;adjacency_list&amp;&nbsp;x)
</pre>
Copy constructor. Creates a new graph that is a copy of graph
<tt>x</tt>, including the edges, vertices, and properties.

<hr>

<pre>
adjacency_list&amp; operator=(const&nbsp;adjacency_list&amp;&nbsp;x)
</pre>
Assignment operator. Makes this graph a copy of graph
<tt>x</tt>, including the edges, vertices, and properties.

<hr>

<pre>
adjacency_list(vertices_size_type&nbsp;n,
               const&nbsp;GraphProperty&amp;&nbsp;p = GraphProperty())
</pre>
Creates a graph object with <TT>n</TT> vertices and zero edges.

<hr>

<a name="sec:iterator-constructor">
<pre>
template &lt;class&nbsp;EdgeIterator&gt;
adjacency_list(EdgeIterator&nbsp;first, EdgeIterator&nbsp;last,
               vertices_size_type&nbsp;n,
               edges_size_type&nbsp;m = 0,
               const&nbsp;GraphProperty&amp;&nbsp;p&nbsp;=&nbsp;GraphProperty())
</pre>
Creates a graph object with <TT>n</TT> vertices and with the edges
specified in the edge list given by the range <TT>[first, last)</TT>.
The <tt>EdgeIterator</tt> must be a model of <a
href="http://www.boost.org/sgi/stl/InputIterator.html">InputIterator</a>.
The value type of the <TT>EdgeIterator</TT> must be a
<TT>std::pair</TT>, 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 <TT>[0, n)</TT>.
</a>

<hr>

<pre>
template &lt;class&nbsp;EdgeIterator, class&nbsp;EdgePropertyIterator&gt;
adjacency_list(EdgeIterator&nbsp;first, EdgeIterator&nbsp;last,
               EdgePropertyIterator&nbsp;ep_iter,
               vertices_size_type&nbsp;n,
               edges_size_type&nbsp;m = 0,
               const&nbsp;GraphProperty&amp;&nbsp;p&nbsp;=&nbsp;GraphProperty())
</pre>
Creates a graph object with <TT>n</TT> vertices and with the edges
specified in the edge list given by the range <TT>[first, last)</TT>.
The <tt>EdgeIterator</tt> and <tt>EdgePropertyIterator</tt> must be a
model of <a
href="http://www.boost.org/sgi/stl/InputIterator.html">InputIterator</a>.
The value type of the <TT>EdgeIterator</TT> must be a
<TT>std::pair</TT>, 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 <TT>[0, n)</TT>. The <TT>value_type</TT> of the
<TT>ep_iter</TT> should be <TT>EdgeProperties</TT>.

<hr>

<pre>
void clear()
</pre>
Remove all of the edges and vertices from the graph.

<hr>

<pre>
void swap(adjacency_list&amp; x)
</pre>
Swap the vertices, edges, and properties of this graph with the
vertices, edges, and properties of graph <tt>x</tt>.
<hr>

<P>

<H2>Non-Member Functions</H2>


<h4>Structure Access</h4>

<hr>

<pre>
std::pair&lt;vertex_iterator,&nbsp;vertex_iterator&gt;
vertices(const adjacency_list&amp; g)
</pre>
Returns an iterator-range providing access to the vertex set of graph
<tt>g</tt>.

<hr>

<pre>
std::pair&lt;edge_iterator,&nbsp;edge_iterator&gt;
edges(const adjacency_list&amp; g)
</pre>
Returns an iterator-range providing access to the edge set of graph
<tt>g</tt>.

<hr>

<pre>
std::pair&lt;adjacency_iterator,&nbsp;adjacency_iterator&gt;
adjacent_vertices(vertex_descriptor&nbsp;u, const&nbsp;adjacency_list&amp;&nbsp;g)
</pre>
Returns an iterator-range providing access to the vertices adjacent to
vertex <tt>u</tt> in graph <tt>g</tt>. For example, if <tt>u -> v</tt>
is an edge in the graph, then <tt>v</tt> will be in this iterator-range.

<hr>

<pre>
std::pair&lt;inv_adjacency_iterator,&nbsp;inv_adjacency_iterator&gt;
inv_adjacent_vertices(vertex_descriptor&nbsp;u, const&nbsp;adjacency_list&amp;&nbsp;g)
</pre>

Returns an iterator-range providing access to the vertices in graph
<tt>g</tt> to which <tt>u</tt> is adjacent. (<tt>inv</tt> is for
inverse.) For example, if <tt>v -> u</tt> is an edge in the graph,
then <tt>v</tt> will be in this iterator range. This function is only
available for bidirectional and undirected <tt>adjacency_list</tt>'s.

<hr>


<pre>
std::pair&lt;out_edge_iterator,&nbsp;out_edge_iterator&gt;
out_edges(vertex_descriptor&nbsp;u, const&nbsp;adjacency_list&amp;&nbsp;g)
</pre>
Returns an iterator-range providing access to the out-edges of vertex
<tt>u</tt> in graph <tt>g</tt>. If the graph is undirected, this
iterator-range provides access to all edges incident on vertex
<tt>u</tt>. For both directed and undirected graphs, for an out-edge
<tt>e</tt>, <tt>source(e, g) == u</tt> and <tt>target(e, g) == v</tt>
where <tt>v</tt> is a vertex adjacent to <tt>u</tt>.

<hr>

<pre>
std::pair&lt;in_edge_iterator,&nbsp;in_edge_iterator&gt;
in_edges(vertex_descriptor&nbsp;v, const&nbsp;adjacency_list&amp;&nbsp;g)
</pre>
Returns an iterator-range providing access to the in-edges of vertex
<tt>v</tt> in graph <tt>g</tt>.  This operation is only available if
<TT>bidirectionalS</TT> was specified for the <TT>Directed</TT>
template parameter. For an in-edge <tt>e</tt>, <tt>target(e, g) == v</tt>
and <tt>source(e, g) == u</tt> for some vertex <tt>u</tt> that is
adjacent to <tt>v</tt>, whether the graph is directed or undirected.

<hr>

<pre>
vertex_descriptor
source(edge_descriptor&nbsp;e, const&nbsp;adjacency_list&amp;&nbsp;g)
</pre>
Returns the source vertex of edge <tt>e</tt>.

<hr>

<pre>
vertex_descriptor
target(edge_descriptor&nbsp;e, const&nbsp;adjacency_list&amp;&nbsp;g)
</pre>
Returns the target vertex of edge <tt>e</tt>.

<hr>

<pre>
degree_size_type
out_degree(vertex_descriptor&nbsp;u, const&nbsp;adjacency_list&amp;&nbsp;g)
</pre>
Returns the number of edges leaving vertex <tt>u</tt>.

<hr>

<pre>
degree_size_type
in_degree(vertex_descriptor&nbsp;u, const&nbsp;adjacency_list&amp;&nbsp;g)
</pre>
Returns the number of edges entering vertex <tt>u</tt>. This operation
is only available if <TT>bidirectionalS</TT> was specified for
the <TT>Directed</TT> template parameter.

<hr>

<pre>
vertices_size_type
num_vertices(const adjacency_list&amp; g)
</pre>
Returns the number of vertices in the graph <tt>g</tt>.

<hr>

<pre>
edges_size_type
num_edges(const adjacency_list&amp; g)
</pre>
Returns the number of edges in the graph <tt>g</tt>.

<hr>

<pre>
vertex_descriptor
vertex(vertices_size_type&nbsp;n, const&nbsp;adjacency_list&amp;&nbsp;g)
</pre>
Returns the nth vertex in the graph's vertex list.

<hr>


<pre>
std::pair&lt;edge_descriptor, bool&gt;
edge(vertex_descriptor&nbsp;u, vertex_descriptor&nbsp;v,
     const&nbsp;adjacency_list&amp;&nbsp;g)
</pre>
If an edge from vertex <tt>u</tt> to vertex <tt>v</tt> exists, return a pair
containing one such edge and <tt>true</tt>.  If there are no edges between
<tt>u</tt> and <tt>v</tt>, return a pair with an arbitrary edge descriptor and
<tt>false</tt>.

<hr>

<pre>
std::pair&lt;out_edge_iterator, out_edge_iterator&gt;
edge_range(vertex_descriptor&nbsp;u, vertex_descriptor&nbsp;v,
           const&nbsp;adjacency_list&amp;&nbsp;g)
</pre>
Returns a pair of out-edge iterators that give the range for
all the parallel edges from <tt>u</tt> to <tt>v</tt>. This
function only works when the <tt>OutEdgeList</tt> for the
<tt>adjacency_list</tt> is a container that sorts the
out edges according to target vertex, and allows for
parallel edges. The <tt>multisetS</tt> selector chooses
such a container.

<hr>

<h4>Structure Modification</h4>

<hr>

<pre>
std::pair&lt;edge_descriptor, bool&gt;
add_edge(vertex_descriptor&nbsp;u, vertex_descriptor&nbsp;v,
         adjacency_list&amp; g)
</pre>
Adds edge <i>(u,v)</i> 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 <TT>bool</TT> flag will be <TT>false</TT>. When the flag is
<TT>false</TT>, the
returned edge descriptor points to the already existing edge.

<p>
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 <tt>OutEdgeList</tt>.

If the <tt>VertexList</tt> selector is
<tt>vecS</tt>, and if either vertex descriptor <tt>u</tt> or
<tt>v</tt> (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 <tt>std::max(u,v) + 1</tt>.

<p>
If the <TT>OutEdgeList</TT> selector is <TT>vecS</TT> then this operation
will invalidate any <tt>out_edge_iterator</tt> for vertex
<i>u</i>. This also applies if the <TT>OutEdgeList</TT> is a user-defined
container that invalidates its iterators when <TT>push(container,
x)</TT> is invoked (see Section <A
HREF="./using_adjacency_list.html#sec:custom-storage">Customizing the
Adjacency List Storage</A>). If the graph is also bidirectional then
any <tt>in_edge_iterator</tt> for <i>v</i> is also invalidated.  If
instead the graph is undirected then any <tt>out_edge_iterator</tt>
for <i>v</i> is also invalidated. If instead the graph is directed,
then <tt>add_edge()</tt> also invalidates any <tt>edge_iterator</tt>.


<hr>

<pre>
std::pair&lt;edge_descriptor,&nbsp;bool&gt;
add_edge(vertex_descriptor&nbsp;u, vertex_descriptor&nbsp;v,
         const&nbsp;EdgeProperties&amp;&nbsp;p,
         adjacency_list&amp;&nbsp;g)
</pre>
Adds edge <i>(u,v)</i> to the graph and attaches <TT>p</TT> as the
value of the edge's internal property storage.  Also see the previous
<TT>add_edge()</TT> non-member function for more details.

<hr>

<pre>
void remove_edge(vertex_descriptor u, vertex_descriptor v,
                 adjacency_list&amp; g)
</pre>
Removes the edge <i>(u,v)</i> from the graph.
<p>
This operation causes any outstanding edge descriptors or iterators
that point to edge <i>(u,v)</i> to become invalid.  In addition, if
the <TT>OutEdgeList</TT> selector is <TT>vecS</TT> then this operation
will invalidate any iterators that point into the edge-list for vertex
<i>u</i> and also for vertex <i>v</i> in the undirected and
bidirectional case. Also, for directed graphs this invalidates any
<tt>edge_iterator</tt>.

<hr>

<pre>
void remove_edge(edge_descriptor e, adjacency_list&amp; g)
</pre>
Removes the edge <tt>e</tt> from the graph. This differs from the
<tt>remove_edge(u, v, g)</tt> function in the case of a
multigraph. This <tt>remove_edge(e, g)</tt> function removes a single
edge, whereas the <tt>remove_edge(u, v, g)</tt> function removes all
edges <i>(u,v)</i>.
<p>
This operation invalidates any outstanding edge descriptors and
iterators for the same edge pointed to by descriptor <tt>e</tt>.  In
addition, this operation will invalidate any iterators that point into
the edge-list for the <tt>target(e, g)</tt>.  Also, for directed
graphs this invalidates any <tt>edge_iterator</tt> for the graph.

<hr>

<pre>
void remove_edge(out_edge_iterator iter, adjacency_list&amp; g)
</pre>
This has the same effect as <tt>remove_edge(*iter, g)</tt>. The
difference is that this function has constant time complexity
in the case of directed graphs, whereas <tt>remove_edge(e, g)</tt>
has time complexity <i>O(E/V)</i>.

<hr>

<pre>
template &lt;class <a href="http://www.boost.org/sgi/stl/Predicate.html">Predicate</a>&gt;
void remove_out_edge_if(vertex_descriptor u, Predicate predicate,
                        adjacency_list&amp; g)
</pre>
Removes all out-edges of vertex <i>u</i> from the graph that satisfy
the <tt>predicate</tt>. That is, if the predicate returns true when
applied to an edge descriptor, then the edge is removed.
<p>
The affect on descriptor and iterator stability is the same as that of
invoking <tt>remove_edge()</tt> on each of the removed edges.

<hr>

<pre>
template &lt;class <a
href="http://www.boost.org/sgi/stl/Predicate.html">Predicate</a>&gt;
void remove_in_edge_if(vertex_descriptor v, Predicate predicate,
                       adjacency_list&amp; g)
</pre>
Removes all in-edges of vertex <i>v</i> from the graph that satisfy
the <tt>predicate</tt>. That is, if the predicate returns true when
applied to an edge descriptor, then the edge is removed.
<p>
The affect on descriptor and iterator stability is the
same as that of invoking <tt>remove_edge()</tt> on each of the
removed edges.
<p>
This operation is available for undirected and bidirectional
<tt>adjacency_list</tt> graphs, but not for directed.

<hr>

<pre>
template &lt;class <a href="http://www.boost.org/sgi/stl/Predicate.html">Predicate</a>&gt;
void remove_edge_if(Predicate predicate, adjacency_list&amp; g)
</pre>
Removes all edges from the graph that satisfy
the <tt>predicate</tt>. That is, if the predicate returns true when
applied to an edge descriptor, then the edge is removed.
<p>
The affect on descriptor and iterator stability is the same as that of
invoking <tt>remove_edge()</tt> on each of the removed edges.

<hr>

<a name="sec:add-vertex">
<pre>
vertex_descriptor
add_vertex(adjacency_list&amp; g)
</pre>
Adds a vertex to the graph and returns the vertex descriptor for the
new vertex.
</a>

<hr>

<pre>
vertex_descriptor
add_vertex(const&nbsp;VertexProperties&amp;&nbsp;p,
           adjacency_list&amp; g)
</pre>
Adds a vertex to the graph with the specified properties. Returns the
vertex descriptor for the new vertex.
</a>

<hr>

<pre>
void clear_vertex(vertex_descriptor u, adjacency_list&amp; g)
</pre>
Removes all edges to and from vertex <i>u</i>. The vertex still appears
in the vertex set of the graph.
<p>
The affect on descriptor and iterator stability is the
same as that of invoking <tt>remove_edge()</tt> for all of
the edges that have <tt>u</tt> as the source or target.

<hr>

<pre>
void clear_out_edges(vertex_descriptor u, adjacency_list&amp; g)
</pre>
Removes all out-edges from vertex <i>u</i>. The vertex still appears
in the vertex set of the graph.
<p>
The affect on descriptor and iterator stability is the
same as that of invoking <tt>remove_edge()</tt> for all of
the edges that have <tt>u</tt> as the source.
<p>
This operation is not applicable to undirected graphs
(use <tt>clear_vertex()</tt> instead).

<hr>

<pre>
void clear_in_edges(vertex_descriptor u, adjacency_list&amp; g)
</pre>
Removes all in-edges from vertex <i>u</i>. The vertex still appears
in the vertex set of the graph.
<p>
The affect on descriptor and iterator stability is the
same as that of invoking <tt>remove_edge()</tt> for all of
the edges that have <tt>u</tt> as the target.
<p>
This operation is only applicable to bidirectional graphs.

<hr>

<pre>
void remove_vertex(vertex_descriptor u, adjacency_list&amp; g)
</pre>
Remove vertex <i>u</i> from the vertex set of the graph. It is assumed
that there are no edges to or from vertex <i>u</i> when it is removed.
One way to make sure of this is to invoke <TT>clear_vertex()</TT>
beforehand.
<p>
If the <TT>VertexList</TT> template parameter of the
<TT>adjacency_list</TT> was <TT>vecS</TT>, then all vertex
descriptors, edge descriptors, and iterators for the graph are
invalidated by this operation. The builtin
<tt>vertex_index_t</tt> property for each vertex is renumbered so that
after the operation the vertex indices still form a contiguous range
<TT>[0, num_vertices(g))</TT>. 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
<TT>remove_vertex()</TT> function the <TT>listS</TT> selector is a
much better choice for the <TT>VertexList</TT> template parameter.

<hr>

<h4><a name="property-map-accessors">Property Map Accessors</a></h4>

<hr>

<pre>
template &lt;class <a href="./PropertyTag.html">PropertyTag</a>&gt;
property_map&lt;adjacency_list, PropertyTag&gt;::type
get(PropertyTag, adjacency_list&amp; g)

template &lt;class <a href="./PropertyTag.html">PropertyTag</a>&gt;
property_map&lt;adjacency_list, Tag&gt;::const_type
get(PropertyTag, const adjacency_list&amp; g)
</pre>
Returns the property map object for the vertex property specified by
<TT>PropertyTag</TT>. The <TT>PropertyTag</TT> must match one of the
properties specified in the graph's <TT>VertexProperty</TT> template
argument.

<hr>

<pre>
template &lt;class <a href="./PropertyTag.html">PropertyTag</a>, class X&gt;
typename property_traits&lt;property_map&lt;adjacency_list, PropertyTag&gt;::const_type&gt::value_type
get(PropertyTag, const adjacency_list&amp; g, X x)
</pre>
This returns the property value for <tt>x</tt>, where <tt>x</tt> is either
a vertex or edge descriptor.
<hr>

<pre>
template &lt;class <a href="./PropertyTag.html">PropertyTag</a>, class X, class Value&gt;
void
put(PropertyTag, const adjacency_list&amp; g, X x, const Value& value)
</pre>
This sets the property value for <tt>x</tt> to
<tt>value</tt>. <tt>x</tt> is either a vertex or edge descriptor.
<tt>Value</tt> must be convertible to
<tt>typename property_traits&lt;property_map&lt;adjacency_list, PropertyTag&gt;::type&gt::value_type</tt>

<hr>

<pre>
template &lt;class GraphProperties, class <a href="./PropertyTag.html#GraphPropertyTag">GraphPropertyTag</a>&gt;
typename graph_property&lt;adjacency_list, GraphPropertyTag&gt;::type&amp;
get_property(adjacency_list&amp; g, GraphPropertyTag);
</pre>
Return the property specified by <tt>GraphPropertyTag</tt> that is
attached to the graph object <tt>g</tt>. The <tt>graph_property</tt>
traits class is defined in <a
href="../../../boost/graph/adjacency_list.hpp"><tt>boost/graph/adjacency_list.hpp</tt></a>.

<hr>

<pre>
template &lt;class GraphProperties, class <a href="./PropertyTag.html#GraphPropertyTag">GraphPropertyTag</a>&gt;
const typename graph_property&lt;adjacency_list, GraphPropertyTag&gt;::type&amp;
get_property(const adjacency_list&amp; g, GraphPropertyTag);
</pre>
Return the property specified by <tt>GraphPropertyTag</tt> that is
attached to the graph object <tt>g</tt>.  The <tt>graph_property</tt>
traits class is defined in <a
href="../../../boost/graph/adjacency_list.hpp"><tt>boost/graph/adjacency_list.hpp</tt></a>.

<!-- add the shortcut property functions -->

<hr>


<h4><a name="serialization">Serialization</a></h4>

<hr>

<pre>
template&lt;class <a href="../../serialization/doc/archives.html#saving_interface">SavingArchive</a>&gt;
SavingArchive&amp; operator<<(SavingArchive&amp; ar, const adjacency_list&amp graph);
</pre>
Serializes the graph into the archive. Requires the vertex and edge properties of the
graph to be <a href="../../serialization/doc/index.html">Serializable</a>.
<br>
Include <a href="../../../boost/graph/adj_list_serialize.hpp"><tt>boost/graph/adj_list_serialize.hpp</tt></a>.
<hr>

<pre>
template&lt;class <a href="../../serialization/doc/archives.html#loading_interface">LoadingArchive</a>&gt;
LoadingArchive&amp; operator>>(LoadingArchive&amp; ar, const adjacency_list&amp graph);
</pre>
Reads the graph from the archive. Requires the vertex and edge properties of the
graph to be <a href="../../serialization/doc/index.html">Serializable</a>.
<br>
Include <a href="../../../boost/graph/adj_list_serialize.hpp"><tt>boost/graph/adj_list_serialize.hpp</tt></a>.
<hr>


<h3>See Also</h3>

<a href="./adjacency_list_traits.html"><tt>adjacency_list_traits</tt></a>,
<a href="./property_map.html"><tt>property_map</tt></a>,
<a href="./graph_traits.html"><tt>graph_traits</tt></a>


<br>
<HR>
<TABLE>
<TR valign=top>
<TD nowrap>Copyright &copy; 2000-2001</TD><TD>
<A HREF="http://www.boost.org/people/jeremy_siek.htm">Jeremy Siek</A>,
Indiana University (<A
HREF="mailto:jsiek@osl.iu.edu">jsiek@osl.iu.edu</A>)<br>
<A HREF="http://www.boost.org/people/liequan_lee.htm">Lie-Quan Lee</A>, Indiana University (<A HREF="mailto:llee@cs.indiana.edu">llee@cs.indiana.edu</A>)<br>
<A HREF="https://homes.cs.washington.edu/~al75">Andrew Lumsdaine</A>,
Indiana University (<A
HREF="mailto:lums@osl.iu.edu">lums@osl.iu.edu</A>)
</TD></TR></TABLE>

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