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<Title>Boost Graph Library: Subgraph</Title>
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<H1><A NAME="sec:subgraph-class"></A>
<pre>
subgraph&lt;Graph&gt;
</pre>
</h1>

<!--The space consumption of the <tt>subgraph</tt> is quite high.
We should change subgraph from representing induced subgraphs to just
normal subgraphs (from talk with Steven North). -->

<p>
The subgraph class provides a mechanism for keeping track of a graph
and its subgraphs. A graph <i>G'</i> is a <i>subgraph</i> of a graph
<i>G</i> if the vertex set of <i>G'</i> is a subset of the vertex set
of <i>G</i> and if the edge set of <i>G'</i> is a subset of the edge
set of <i>G</i>. That is, if <i>G'=(V',E')</i> and <i>G=(V,E)</i>,
then <i>G'</i> is a subgraph of <i>G</i> if <i>V'</i> is a subset of
<i>V</i> and <i>E</i> is a subset of <i>E'</i>. An <i>induced
subgraph</i> is a subgraph formed by specifying a set of vertices
<i>V'</i> and then selecting all of the edges from the original graph
that connect two vertices in <i>V'</i>. So in this case <i>E' = {(u,v)
in E: u,v in V'}</i>.  Figure 1 shows a graph <i>G<sub>0</sub></i> and
two subgraphs <i>G<sub>1</sub></i> and <i>G<sub>2</sub></i>. The edge
set for <i>G<sub>1</sub></i> is <i>E<sub>1</sub> = { (E,F), (C,F)
}</i> and the edge set for <i>G<sub>2</sub></i> is <i>E<sub>2</sub> =
{ (A,B) }</i>. Edges such as <i>(E,B)</i> and <i>(F,D)</i> that cross
out of a subgraph are not in the edge set of the subgraph.
</p>

<P></P>
<DIV ALIGN="center"><A NAME="fig:subgraph-tree"></A>
<TABLE>
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 1:</STRONG> A graph with nested subgraphs, maintained in a tree structure.</CAPTION>
<TR><TD><IMG SRC="./figs/subgraph.gif"></TD>
<TD><IMG SRC="./figs/subgraph-tree.gif"></TD></TR>
</TABLE>
</DIV><P></P>

<p>The <tt>subgraph</tt> class implements induced subgraphs. The main graph
and its subgraphs are maintained in a tree data structure. The main
graph is the root, and subgraphs are either children of the root or of
other subgraphs. All of the nodes in this tree, including the root
graph, are instances of the <tt>subgraph</tt> class.  The
<tt>subgraph</tt> implementation ensures that each node in the tree is
an induced subgraph of its parent. The <tt>subgraph</tt> class
implements the BGL graph interface, so each subgraph object can be
treated as a graph.</p>

<h3>Example</h3>

The full source code for this example is in
<tt>example/subgraph.cpp</tt>. To create a graph and subgraphs, first
create the root graph object.  Here we use <tt>adjacency_list</tt> as
the underlying graph implementation. The underlying graph type is
required to have <tt>vertex_index</tt> and <tt>edge_index</tt>
internal properties, so we add an edge index property to the adjacency
list. We do not need to add a vertex index property because that is
built in to the <tt>adjacency_list</tt>. We will be building the graph
and subgraphs in Figure 1, so we will need a total of six vertices.

<pre>
typedef adjacency_list_traits&lt; vecS, vecS, directedS &gt; Traits;
typedef subgraph&lt; adjacency_list&lt; vecS, vecS, directedS,
  no_property, property&lt; edge_index_t, int &gt; &gt; &gt; Graph;

const int N = 6;
Graph G0(N);

enum { A, B, C, D, E, F};  // for conveniently referring to vertices in G0
</pre>

Next we create two empty subgraph objects, specifying <tt>G0</tt> as
their parent.

<pre>
Graph& G1 = G0.create_subgraph(), G2 = G0.create_subgraph();
enum { A1, B1, C1 }; // for conveniently referring to vertices in G1
enum { A2, B2 };     // for conveniently referring to vertices in G2
</pre>

We can add vertices from the root graph to the subgraphs using the
<tt>add_vertex</tt> function. Since the graph implementation is
<tt>adjacency_list</tt> with <tt>VertexList=vecS</tt>, we can use the
integers (or in this case enums) in the range <i>[0,6)</i> as vertex
descriptors.

<pre>
add_vertex(C, G1); // global vertex C becomes local A1 for G1
add_vertex(E, G1); // global vertex E becomes local B1 for G1
add_vertex(F, G1); // global vertex F becomes local C1 for G1

add_vertex(A, G2); // global vertex A becomes local A2 for G2
add_vertex(B, G2); // global vertex B becomes local B2 for G2
</pre>

Next we can add edges to the main graph using the usual
<tt>add_edge</tt> function.

<pre>
add_edge(A, B, G0);
add_edge(B, C, G0);
add_edge(B, D, G0);
add_edge(E, B, G0);
add_edge(E, F, G0);
add_edge(F, D, G0);
</pre>

We can also add edges to subgraphs such as <tt>G1</tt> using the
<tt>add_edge</tt> function. Each subgraph has its own vertex and edge
descriptors, which we call <i>local</i> descriptors. We refer to root
graph's vertex and edge descriptors as the <i>global</i>
descriptors. Above, we used global vertex descriptors to add vertices
to the graph. However, most <tt>subgraph</tt> functions work with
local descriptors. So in the following call to <tt>add_edge</tt> we
add the edge <tt>(A1,C1)</tt> (or numerically <tt>(0,2)</tt>) which is
the local version (for subgraph <tt>G1</tt>) of the global edge
<tt>(C,F)</tt> (or numerically <tt>(2,5)</tt>).  Adding an edge to a
subgraph causes the edge to also be added to all of its ancestors in
the subgraph tree to ensure that the subgraph property is maintained.

<pre>
add_edge(A1, C1, G1); // (A1,C1) is subgraph G1 local indices
                      // for the global edge (C,F).
</pre>

<!----------------------------->
<h3>Where Defined</h3>

<tt>boost/graph/subgraph.hpp</tt>

<!----------------------------->
<h3>Template Parameters</h3>

<P>
<TABLE border>
<TR>
<th>Parameter</th><th>Description</th>
</tr>
<tr><td><tt>Graph</tt> </td>
<td> A graph type modeling <a href="VertexMutableGraph.html">VertexMutableGraph</a>
  and <a href="EdgeMutableGraph.html">EdgeMutableGraph</a>. Also
  the graph must have internal <tt>vertex_index</tt> and
  <tt>edge_index</tt> properties. The vertex indices must be maintained
  automatically by the graph, whereas the edge indices will be
  assigned by the <tt>subgraph</tt> class implementation. </td>
</tr>
</table>


<!----------------------------->
<h3>Model Of</h3>

<tt>subgraph</tt> is a model of <a href="VertexMutableGraph.html">VertexMutableGraph</a>. Also, if
the <tt>Graph</tt> type models <a href="VertexListGraph.html">VertexListGraph</a>,
<a href="EdgeListGraph.html">EdgeListGraph</a> and/or <a href="BidirectionalGraph.html">BidirectionalGraph</a>, then
<tt>subgraph&lt;Graph&gt;</tt> will also models these concepts.

<!----------------------------->
<h3>Associated Types</h3>

If the graph is the root of the subgraph tree, then the vertex and
edge descriptors are both the local descriptors for the root graph,
and they are the global descriptors. If the graph is not the root,
then the descriptors are local descriptors for the subgraph.
The subgraph iterators are the same iterator types as the iterators of
the underlying <tt>Graph</tt> type.

<hr>

<pre>
graph_traits&lt;subgraph&gt;::vertex_descriptor
</pre>
    The type for the vertex descriptors.
 (Required by <a href="Graph.html">Graph</a>.)

<hr>

<pre>
graph_traits&lt;subgraph&gt;::edge_descriptor
</pre>
    The type for the edge descriptors.
    (Required by <a href="Graph.html">Graph</a>.)

<hr>

<pre>
graph_traits&lt;subgraph&gt;::vertex_iterator
</pre>
    The type for the iterators returned by <tt>vertices</tt>.
    (Required by <a href="VertexListGraph.html">VertexListGraph</a>.)

<hr>

<pre>
graph_traits&lt;subgraph&gt;::edge_iterator
</pre>
    The type for the iterators returned by <tt>edges</tt>.
    (Required by <a href="EdgeListGraph.html">EdgeListGraph</a>.)

<hr>
<pre>
graph_traits&lt;subgraph&gt;::out_edge_iterator
</pre>
    The type for the iterators returned by <tt>out_edges</tt>.
    (Required by <a href="IncidenceGraph.html">IncidenceGraph</a>.)

<hr>
<pre>
graph_traits&lt;subgraph&gt;::in_edge_iterator
</pre>
    The <tt>in_edge_iterator</tt> is the
    iterator type returned by the <tt>in_edges</tt> function.
    (Required by <a href="BidirectionalGraph.html">BidirectionalGraph</a>.)

<hr>
<pre>
graph_traits&lt;subgraph&gt;::adjacency_iterator
</pre>
    The type for the iterators returned by <tt>adjacent_vertices</tt>.
    (Required by <a href="AdjacencyGraph.html">AdjacencyGraph</a>.)

<hr>
<pre>
graph_traits&lt;subgraph&gt;::directed_category
</pre>
    Provides information about whether the graph is directed
    (<tt>directed_tag</tt>) or undirected (<tt>undirected_tag</tt>).
    (Required by <a href="Graph.html">Graph</a>.)

<hr>
<pre>
graph_traits&lt;subgraph&gt;::edge_parallel_category
</pre>
    This describes whether the graph class allows the insertion of
    parallel edges (edges with the same source and target), which
    depends on the underlying <tt>Graph</tt> class. The two tags are
    <tt>allow_parallel_edge_tag</tt> and
    <tt>disallow_parallel_edge_tag</tt>.
    (Required by <a href="Graph.html">Graph</a>.)

<hr>
<pre>
graph_traits&lt;subgraph&gt;::vertices_size_type
</pre>
  The type used for dealing with the number of vertices in
  the graph.
  (Required by <a href="VertexListGraph.html">VertexListGraph</a>.)

<hr>
<pre>
graph_traits&lt;subgraph&gt;::edges_size_type
</pre>
  The type used for dealing with the number of edges in the graph.
  (Required by <a href="EdgeListGraph.html">EdgeListGraph</a>.)

<hr>
<pre>
graph_traits&lt;subgraph&gt;::degree_size_type
</pre>
  The type used for dealing with the number of out-edges of a vertex.
  (Required by <a href="IncidenceGraph.html">IncidenceGraph</a>.)

<hr>
<pre>
property_map&lt;subgraph, PropertyTag&gt;::type
property_map&lt;subgraph, PropertyTag&gt;::const_type
</pre>
  The map type for vertex or edge properties in the graph. The
  specific property is specified by the <tt>PropertyTag</tt> template
  argument, and must match one of the properties specified in the
  <tt>VertexProperty</tt> or <tt>EdgeProperty</tt> for the graph.
  (Required by <a href="PropertyGraph.html">PropertyGraph</a>.)

<hr>
<pre>
subgraph::children_iterator
</pre>
  The iterator type for accessing the children subgraphs of the graph.


<!----------------------------->
<h3>Member Functions</h3>


<hr>
<pre>
subgraph(vertices_size_type n, const GraphProperty&amp; p = GraphProperty())
</pre>
    Creates the root graph object with <tt>n</tt> vertices and zero edges.

<hr>
<pre>
subgraph&lt;Graph&gt;& create_subgraph();
</pre>
    Creates an empty subgraph object whose parent is <i>this</i>
    graph.

<hr>
<pre>
template &lt;typename VertexIterator&gt;
subgraph&lt;Graph&gt;&amp;
create_subgraph(VertexIterator first, VertexIterator last)
</pre>
    Creates a subgraph object with the specified vertex set.  The
    edges of the subgraph are induced by the vertex set. That is,
    every edge in the parent graph (which is <i>this</i> graph) that
    connects two vertices in the subgraph will be added to the
    subgraph.

<hr>
<pre>
vertex_descriptor local_to_global(vertex_descriptor u_local) const
</pre>
    Converts a local vertex descriptor to the corresponding global
    vertex descriptor.

<hr>
<pre>
vertex_descriptor global_to_local(vertex_descriptor u_global) const
</pre>
    Converts a global vertex descriptor to the corresponding local
    vertex descriptor.

<hr>
<pre>
edge_descriptor local_to_global(edge_descriptor e_local) const
</pre>
    Converts a local edge descriptor to the corresponding global edge
    descriptor.

<hr>
<pre>
edge_descriptor global_to_local(edge_descriptor u_global) const
</pre>
    Converts a global edge descriptor to the corresponding local edge
    descriptor.

<hr>
<pre>
std::pair&lt;vertex_descriptor, bool&gt; find_vertex(vertex_descriptor u_global) const
</pre>
    If vertex <i>u</i> is in this subgraph, the function returns the local
    vertex descriptor that corresponds to the global vertex descriptor
    <tt>u_global</tt> as the first part of the pair and <tt>true</tt> for
    the second part of the pair. If vertex <i>u</i> is not in the subgraph
    then this function returns false in the second part of the
    pair.

<hr>
<pre>
subgraph& root()
</pre>
    Returns the root graph of the subgraph tree.

<hr>
<pre>
bool is_root() const
</pre>
    Return <tt>true</tt> if the graph is the root of the subgraph tree,
    and returns <tt>false</tt> otherwise.

<hr>
<pre>
subgraph& parent()
</pre>
    Returns the parent graph.

<hr>
<pre>
std::pair&lt;children_iterator, children_iterator&gt; children() const
</pre>
Return an iterator pair for accessing the children subgraphs.


<!----------------------------->
<h3>Nonmember Functions</h3>

The functionality of <tt>subgraph</tt> depends on the
<tt>Graph</tt> type. For example, if <tt>Graph</tt> in a
<a href="BidirectionalGraph.html">BidirectionalGraph</a> and supports <tt>in_edges</tt>, then so
does <tt>subgraph</tt>. Here we list all the functions that
<tt>subgraph</tt> could possibly support given a <tt>Graph</tt>
type that is a model of <a href="VertexListGraph.html">VertexListGraph</a>, <a href="EdgeListGraph.html">EdgeListGraph</a> and
<a href="BidirectionalGraph.html">BidirectionalGraph</a>. If the <tt>Graph</tt> type that you use
with <tt>subgraph</tt> does not model these concepts and supports
fewer functions, then the <tt>subgraph</tt> will also support
fewer functions and some of the functions listed below will not be
implemented.


<hr>
<pre>
std::pair&lt;vertex_iterator, vertex_iterator&gt;
vertices(const subgraph&amp; g)
</pre>
    Returns an iterator range providing access to the vertex set of subgraph <i>g</i>.
    (Required by <a href="VertexListGraph.html">VertexListGraph</a>.)

<hr>
<pre>
std::pair&lt;edge_iterator, edge_iterator&gt;
edges(const subgraph&amp; g)
</pre>
    Returns an iterator range providing access to the edge set of subgraph <i>g</i>.
    (Required by <a href="EdgeListGraph.html">EdgeListGraph</a>.)

<hr>
<pre>
std::pair&lt;adjacency_iterator, adjacency_iterator&gt;
adjacent_vertices(vertex_descriptor u_local, const subgraph&amp; g)
</pre>
    Returns an iterator range providing access to the vertices
    adjacent to
    vertex <i>u</i> in subgraph <i>g</i>.
    (Required by <a href="AdjacencyGraph.html">AdjacencyGraph</a>.)

<hr>
<pre>
std::pair&lt;out_edge_iterator, out_edge_iterator&gt;
out_edges(vertex_descriptor u_local, const subgraph&amp; g)
</pre>
    Returns an iterator range providing access to the out-edges of
    vertex <i>u</i> in subgraph <i>g</i>. If the graph is undirected, this
    iterator range provides access to all edge incident on
    vertex <i>u</i>.
    (Required by <a href="IncidenceGraph.html">IncidenceGraph</a>.)

<hr>
<pre>
std::pair&lt;in_edge_iterator, in_edge_iterator&gt;
in_edges(vertex_descriptor v_local, const subgraph&amp; g)
</pre>
    Returns an iterator range providing access to the in-edges of
    vertex
    <i>v</i> in subgraph <i>g</i>.
    (Required by <a href="BidirectionalGraph.html">BidirectionalGraph</a>.)

<hr>
<pre>
vertex_descriptor
source(edge_descriptor e_local, const subgraph&amp; g)
</pre>
    Returns the source vertex of edge <i>e</i> in subgraph <i>g</i>.
    (Required by <a href="IncidenceGraph.html">IncidenceGraph</a>.)

<hr>
<pre>
vertex_descriptor
target(edge_descriptor e_local, const subgraph&amp; g)
</pre>
    Returns the target vertex of edge <i>e</i> in subgraph <i>g</i>.
    (Required by <a href="IncidenceGraph.html">IncidenceGraph</a>.)

<hr>
<pre>
degree_size_type
out_degree(vertex_descriptor u_local, const subgraph&amp; g)
</pre>
    Returns the number of edges leaving vertex <i>u</i> in subgraph <i>g</i>.
    (Required by <a href="IncidenceGraph.html">IncidenceGraph</a>.)

<hr>
<pre>
degree_size_type in_degree(vertex_descriptor u_local, const subgraph&amp; g)
</pre>
    Returns the number of edges entering vertex <i>u</i> in subgraph <i>g</i>.
    (Required by <a href="BidirectionalGraph.html">BidirectionalGraph</a>.)

<hr>
<pre>
vertices_size_type num_vertices(const subgraph&amp; g)
</pre>
    Returns the number of vertices in the subgraph <i>g</i>.
    (Required by <a href="VertexListGraph.html">VertexListGraph</a>.)

<hr>
<pre>
edges_size_type num_edges(const subgraph&amp; g)
</pre>
    Returns the number of edges in the subgraph <i>g</i>.  (Required by
    <a href="EdgeListGraph.html">EdgeListGraph</a>.)

<hr>
<pre>
vertex_descriptor vertex(vertices_size_type n, const subgraph&amp; g)
</pre>
    Returns the <i>n</i>th vertex in the subgraph's vertex list.

<hr>
<pre>
std::pair&lt;edge_descriptor, bool&gt;
edge(vertex_descriptor u_local, vertex_descriptor v_local, const subgraph&amp; g)
</pre>
    Returns the edge connecting vertex <i>u</i> to vertex <i>v</i> in subgraph <i>g</i>.
    (Required by <a href="AdjacencyMatrix.html">AdjacencyMatrix</a>.)


<hr>
<pre>
std::pair&lt;edge_descriptor, bool&gt;
add_edge(vertex_descriptor u_local, vertex_descriptor v_local, subgraph&amp; g)
</pre>
    Adds edge <i>(u,v)</i> to the subgraph <i>g</i> and to all of the subgraph's
    ancestors in the subgraph tree. This function returns the edge
    descriptor for the new edge. If the edge is already in the graph
    then a duplicate will not be added and the Boolean flag will be
    false.
    (Required by <a href="EdgeMutableGraph.html">EdgeMutableGraph</a>.)

<hr>
<pre>
std::pair&lt;edge_descriptor, bool&gt;
add_edge(vertex_descriptor u_local, vertex_descriptor v_local,
         const EdgeProperty&amp; p, subgraph&amp; 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> member function for more details.

<hr>
<pre>
void remove_edge(vertex_descriptor u_local, vertex_descriptor v_local,
                 subgraph&amp; g)
</pre>
    Removes the edge <i>(u,v)</i> from the subgraph and from all of the
    ancestors of <tt>g</tt> in the subgraph tree.
    (Required by <a href="EdgeMutableGraph.html">EdgeMutableGraph</a>.)

<hr>
<pre>
void remove_edge(edge_descriptor e_local, subgraph&amp; g)
</pre>
    Removes the edge <tt>e</tt> from the subgraph and from all of the
    ancestors of <tt>g</tt> in the subgraph tree.
    (Required by <a href="EdgeMutableGraph.html">EdgeMutableGraph</a>.)

<hr>
<pre>
vertex_descriptor
add_vertex(subgraph&amp; g)
</pre>
    Adds a vertex to the subgraph and returns the vertex descriptor
    for the new vertex. The vertex is also added to all ancestors of
    <tt>g</tt> in the subgraph tree to maintain the subgraph property.
    (Required by <a href="VertexMutableGraph.html">VertexMutableGraph</a>.)

<hr>
<pre>
vertex_descriptor
add_vertex(vertex_descriptor u_global, subgraph&amp; g)
</pre>
Adds the vertex <i>u</i> from the root graph to the subgraph <tt>g</tt>.
(Required by <a href="VertexMutableGraph.html">VertexMutableGraph</a>.)


<hr>
<pre>
template &lt;class PropertyTag&gt;
property_map&lt;subgraph, PropertyTag&gt;::type
get(PropertyTag, subgraph&amp; g)

template &lt;class PropertyTag&gt;
property_map&lt;subgraph, PropertyTag&gt;::const_type
get(PropertyTag, const subgraph&amp; g)
</pre>
    Returns the property map object for the vertex or edge property
    specified by <tt>PropertyTag</tt>. The <tt>PropertyTag</tt> must match one
    of the properties specified in the graph's <tt>PropertyTag</tt>
    template argument.  Vertex and edge properties are shared by all
    subgraphs, so changes to a property through a local vertex
    descriptor for one subgraph will change the property for the
    global vertex descriptor, and therefore for all other subgraphs.
    However, the key type for a subgraph's property map is a subgraph-local
    vertex or  edge descriptor.
    (Required by <a href="PropertyGraph.html">PropertyGraph</a>.)

<hr>
<pre>
template &lt;class PropertyTag, class Key&gt;
typename property_traits&lt;
  typename property_map&lt;subgraph, PropertyTag&gt;::const_type
&gt;::value_type
get(PropertyTag, const subgraph&amp; g, Key k_local)
</pre>
    This returns the property value for the key <tt>k_local</tt>, which
    is either a local vertex or local edge descriptor. See the above
    <tt>get</tt> function
    for more information about the property maps.
    (Required by <a href="PropertyGraph.html">PropertyGraph</a>.)

<hr>
<pre>
template &lt;class PropertyTag, class Key, class Value&gt;
void
put(PropertyTag, const subgraph&amp; g, Key k_local, const Value& value)
</pre>
    This sets the property value for the key <tt>k_local</tt> to
    <tt>value</tt>.  <tt>k_local</tt> is either a local vertex or local
    edge descriptor.  <tt>Value</tt> must be convertible to
    <tt>typename
      property_traits&lt;property_map&lt;adjacency_matrix,
      PropertyTag&gt;::type&gt;::value_type</tt>.
    (Required by <a href="PropertyGraph.html">PropertyGraph</a>.)

<hr>
<pre>
template &lt;class GraphProperties, class GraphPropertyTag&gt;
typename property_value&lt;GraphProperties, GraphPropertyTag&gt;::type&amp;
get_property(subgraph&amp; g, GraphPropertyTag);
</pre>
Return the property specified by <tt>GraphPropertyTag</tt> that is attached
to the subgraph object <tt>g</tt>. The <tt>property_value</tt> traits class
is defined in <tt>boost/pending/property.hpp</tt>.


<hr>
<pre>
template &lt;class GraphProperties, class GraphPropertyTag&gt;
const typename property_value&lt;GraphProperties, GraphPropertyTag&gt;::type&amp;
get_property(const subgraph&amp; g, GraphPropertyTag);
</pre>
Return the property specified by <tt>GraphPropertyTag</tt> that is
attached to the subgraph object <tt>g</tt>.  The <tt>property_value</tt>
traits class is defined in <tt>boost/pending/property.hpp</tt>.

<hr>
<h2>Notes</h2>
The subgraph template requires the underlying graph type to supply vertex and
edge index properties. However, there is no default constructor of any adjacency
list that satisfies both of these requirements. This is especially true of graphs
using <a href="bundles.html">bundled properties</a>, or any adjacency list whose
vertex set is selected by anything other that <tt>vecS</tt>.

However, this problem can be overcome by embedding your bundled (or otherwise)
properties into a <tt>property</tt> that contains an appropriate index. For
example:
<pre>
struct my_vertex { ... };
typedef property&lt;vertex_index_t, std::size_t, my_vertex&gt; vertex_prop;

struct my_edge { ... };
typedef property&lt;edge_index_t, std::size_t, my_edge&gt; edge_prop;

typedef adjacency_list&lt;vecS, listS, undirectedS, vertex_prop, edge_prop&gt; Graph;
typedef subgraph&lt;Graph&gt; Subgraph;
</pre>