585 lines
19 KiB
HTML
585 lines
19 KiB
HTML
<HTML>
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<!--
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Copyright (c) Jeremy Siek 2000
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Distributed under the Boost Software License, Version 1.0.
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(See accompanying file LICENSE_1_0.txt or copy at
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http://www.boost.org/LICENSE_1_0.txt)
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-->
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<Head>
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<Title>Boost Graph Library: Adjacency Matrix</Title>
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<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
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ALINK="#ff0000">
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<IMG SRC="../../../boost.png"
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ALT="C++ Boost" width="277" height="86">
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<BR Clear>
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<H1><A NAME="sec:adjacency-matrix-class"></A>
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<pre>
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adjacency_matrix<Directed, VertexProperty,
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EdgeProperty, GraphProperty,
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Allocator>
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</pre>
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</H1>
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The <tt>adjacency_matrix</tt> class implements the BGL graph interface
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using the traditional adjacency matrix storage format. For a graph
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with <i>V</i> vertices, a <i>V x V</i> matrix is used, where each
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element <i>a<sub>ij</sub></i> is a boolean flag that says whether
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there is an edge from vertex <i>i</i> to vertex <i>j</i>. <a
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href="#fig:adj-matrix-graph">Figure 1</a> shows the adjacency matrix
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representation of a graph.
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<P></P>
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<DIV ALIGN="center"><A NAME="fig:adj-matrix-graph"></A>
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<TABLE>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure 1:</STRONG> Adjacency Matrix Representation of a Directed Graph.</CAPTION>
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<TR><TD><IMG SRC="./figs/adj-matrix-graph3.gif" width="386" height="284"></TD>
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<TD><IMG SRC="./figs/adj-matrix.gif" width="135" height="136"></TD></TR>
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</TABLE>
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</DIV><P></P>
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The advantage of this matrix format over the adjacency list is that
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edge insertion and removal is constant time. There are several
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disadvantages. The first is that the amount of memory used is
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<i>O(V<sup>2</sup>)</i> instead of <i>O(V + E)</i> (where <i>E</i> is
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the number of edges). The second is that operations that traverse all
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the out-edges of each vertex (such as breadth-first search) run in
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<i>O(V<sup>2</sup>)</i> time instead of <i>O(V + E)</i> time for the
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adjacency list. In short, it is better to use the
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<tt>adjacency_matrix</tt> for dense graphs (where <i>E</i> is close to
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<i>V<sup>2</sup></i>) and it is better to use <a
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href="adjacency_list.html"><tt>adjacency_list</tt></a> for sparse
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graphs (where <i>E</i> is much smaller than <i>V<sup>2</sup></i>).
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The <tt>adjacency_matrix</tt> class extends the traditional
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data-structure by allowing objects to be attached to vertices and
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edges using the same property template parameters supported by <a
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href="adjacency_list.html"><tt>adjacency_list</tt></a>. These may be
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<a href="bundles.html">bundled properties</a> or standard (backward-compatible)
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<a
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href="using_adjacency_list.html#sec:adjacency-list-properties">interior
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properties</a>. The types of all property values must be
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Copy Constructible, Assignable and Default Constructible.
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In the case of an undirected graph, the
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<tt>adjacency_matrix</tt>. class does not use a full <i>V x V</i>
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matrix but instead uses a lower triangle (the diagonal and below)
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since the matrix for an undirected graph is symmetric. This reduces
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the storage to <i>(V<sup>2</sup>)/2</i>. <a
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href="#fig:undir-adj-matrix-graph">Figure 2</a> shows an adjacency
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matrix representation of an undirected graph.
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<P></P>
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<DIV ALIGN="center"><A NAME="fig:undir-adj-matrix-graph"></A>
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<TABLE>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure 2:</STRONG> Adjacency Matrix Representation of an Undirected Graph.</CAPTION>
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<TR><TD><IMG SRC="./figs/undir-adj-matrix-graph3.gif" width="260" height="240"></TD>
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<TD><IMG SRC="./figs/undir-adj-matrix2.gif" width="135" height="136"></TD></TR>
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</TABLE>
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</DIV><P></P>
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<h3>Example</h3>
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Creating the graph of <a href="#fig:adj-matrix-graph">Figure 1</a>.
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<pre>
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enum { A, B, C, D, E, F, N };
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const char* name = "ABCDEF";
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typedef boost::adjacency_matrix<boost::directedS> Graph;
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Graph g(N);
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add_edge(B, C, g);
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add_edge(B, F, g);
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add_edge(C, A, g);
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add_edge(C, C, g);
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add_edge(D, E, g);
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add_edge(E, D, g);
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add_edge(F, A, g);
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std::cout << "vertex set: ";
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boost::print_vertices(g, name);
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std::cout << std::endl;
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std::cout << "edge set: ";
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boost::print_edges(g, name);
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std::cout << std::endl;
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std::cout << "out-edges: " << std::endl;
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boost::print_graph(g, name);
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std::cout << std::endl;
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</pre>
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The output is:
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<pre>
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vertex set: A B C D E F
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edge set: (B,C) (B,F) (C,A) (C,C) (D,E) (E,D) (F,A)
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out-edges:
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A -->
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B --> C F
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C --> A C
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D --> E
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E --> D
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F --> A
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</pre>
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Creating the graph of <a href="#fig:undir-adj-matrix-graph">Figure 2</a>.
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<pre>
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enum { A, B, C, D, E, F, N };
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const char* name = "ABCDEF";
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typedef boost::adjacency_matrix<boost::undirectedS> UGraph;
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UGraph ug(N);
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add_edge(B, C, ug);
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add_edge(B, F, ug);
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add_edge(C, A, ug);
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add_edge(D, E, ug);
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add_edge(F, A, ug);
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std::cout << "vertex set: ";
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boost::print_vertices(ug, name);
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std::cout << std::endl;
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std::cout << "edge set: ";
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boost::print_edges(ug, name);
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std::cout << std::endl;
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std::cout << "incident edges: " << std::endl;
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boost::print_graph(ug, name);
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std::cout << std::endl;
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</pre>
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The output is:
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<pre>
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vertex set: A B C D E F
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edge set: (C,A) (C,B) (E,D) (F,A) (F,B)
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incident edges:
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A <--> C F
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B <--> C F
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C <--> A B
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D <--> E
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E <--> D
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F <--> A B
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</pre>
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<h3>Where Defined</h3>
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<a href="../../../boost/graph/adjacency_matrix.hpp"><tt>boost/graph/adjacency_matrix.hpp</tt></a>
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<h3>Template Parameters</h3>
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<p>
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<table border>
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<TR>
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<th>Parameter</th><th>Description</th><th>Default</th>
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</tr>
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<tr>
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<td><tt>Directed</tt></td>
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<td>A selector to choose whether the graph is directed or undirected. The options are <tt>directedS</tt> and <tt>undirectedS</tt>.</td>
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<td><tt>directedS</tt></td>
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</tr>
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<tr>
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<td><tt>VertexProperty</tt></td>
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<td>for specifying internal property storage.</td>
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<td><tt>no_property</tt></td>
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</tr>
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<tr>
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<td><tt>EdgeProperty</tt></td>
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<td>for specifying internal property storage.</td>
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<td><tt>no_property</tt></td>
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</tr>
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<tr>
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<td><tt>GraphProperty</tt></td>
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<td>for specifying property storage for the graph object.</td>
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<td><tt>no_property</tt></td>
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</tr>
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</table>
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<h3>Model Of</h3>
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<a href="./VertexAndEdgeListGraph.html">VertexAndEdgeListGraph</a>,
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<a href="./IncidenceGraph.html">Incidence Graph</a>,
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<a href="./BidirectionalGraph.html">Bidirectional Graph</a>,
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<a
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href="./AdjacencyMatrix.html">AdjacencyMatrix</a>, <a
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href="./MutablePropertyGraph.html">MutablePropertyGraph</a>,
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<a href="../../utility/CopyConstructible.html">CopyConstructible</a>,
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and <a href="../../utility/Assignable.html">Assignable</a>.
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<h3>Associated Types</h3>
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<hr>
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<tt>graph_traits<adjacency_matrix>::vertex_descriptor</tt>
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<br><br>
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The type for the vertex descriptors associated with the
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<tt>adjacency_matrix</tt>.<br>
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(Required by <a href="./Graph.html">Graph</a>.)
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<hr>
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<tt>graph_traits<adjacency_matrix>::edge_descriptor</tt>
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<br><br>
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The type for the edge descriptors associated with the
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<tt>adjacency_matrix</tt>.<br>
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(Required by <a href="Graph.html">Graph</a>.)
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<hr>
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<tt>graph_traits<adjacency_matrix>::vertex_iterator</tt>
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<br><br>
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The type for the iterators returned by <tt>vertices()</tt>.
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The vertex iterator models <a href="http://www.boost.org/sgi/stl/RandomAccessIterator.html">RandomAccessIterator</a>. <br>
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(Required by <a href="VertexListGraph.html">VertexListGraph</a>.)
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<hr>
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<tt>graph_traits<adjacency_matrix>::edge_iterator</tt>
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<br><br>
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The type for the iterators returned by <tt>edges()</tt>. This
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iterator models <a href="../../utility/MultiPassInputIterator.html">MultiPassInputIterator</a>.<br>
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(Required by <a href="EdgeListGraph.html">EdgeListGraph</a>.)
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<hr>
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<tt>graph_traits<adjacency_matrix>::out_edge_iterator</tt>
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<br><br>
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The type for the iterators returned by <tt>out_edges()</tt>. This
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iterator models <a href="../../utility/MultiPassInputIterator.html">MultiPassInputIterator</a>. <br>
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(Required by <a href="IncidenceGraph.html">IncidenceGraph</a>.)
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<hr>
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<tt>graph_traits<adjacency_matrix>::in_edge_iterator</tt>
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<br><br>
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The type for the iterators returned by <tt>in_edges()</tt>. This
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iterator models <a href="../../utility/MultiPassInputIterator.html">MultiPassInputIterator</a>. <br>
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(Required by <a href="BidirectionalGraph.html">BidirectionalGraph</a>.)
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<hr>
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<tt>graph_traits<adjacency_matrix>::adjacency_iterator</tt>
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<br><br>
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The type for the iterators returned by <tt>adjacent_vertices()</tt>. This
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iterator models the same concept as the out-edge iterator.<br>
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(Required by <a href="AdjacencyGraph.html">AdjacencyGraph</a>.)
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<hr>
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<tt>graph_traits<adjacency_matrix>::directed_category</tt>
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<br><br>
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Provides information about whether the graph is directed
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(<tt>directed_tag</tt>) or undirected (<tt>undirected_tag</tt>).<br>
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(Required by <a href="Graph.html">Graph</a>.)
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<hr>
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<tt>graph_traits<adjacency_matrix>::edge_parallel_category</tt>
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<br><br>
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An adjacency matrix does not allow the insertion of
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parallel edges, so this type is always
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<tt>disallow_parallel_edge_tag</tt>. <br>
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(Required by <a href="Graph.html">Graph</a>.)
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<hr>
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<tt>graph_traits<adjacency_matrix>::vertices_size_type</tt>
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<br><br>
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The type used for dealing with the number of vertices in
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the graph.<br>
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(Required by <a href="VertexListGraph.html">VertexListGraph</a>.)
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<hr>
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<tt>graph_traits<adjacency_matrix>::edges_size_type</tt>
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<br><br>
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The type used for dealing with the number of edges in the graph.<br>
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(Required by <a href="EdgeListGraph.html">EdgeListGraph</a>.)
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<hr>
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<tt>graph_traits<adjacency_matrix>::degree_size_type</tt>
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<br><br>
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The type used for dealing with the number of out-edges of a vertex.<br>
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(Required by <a href="IncidenceGraph.html">IncidenceGraph</a>.)
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<hr>
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<tt>property_map<adjacency_matrix, PropertyTag>::type</tt><br>
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<tt>property_map<adjacency_matrix, PropertyTag>::const_type</tt>
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<br><br>
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The map type for vertex or edge properties in the graph. The
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specific property is specified by the <tt>PropertyTag</tt> template
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argument, and must match one of the properties specified in the
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<tt>VertexProperty</tt> or <tt>EdgeProperty</tt> for the graph.<br>
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(Required by <a href="PropertyGraph.html">PropertyGraph</a>.)
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<hr>
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<h3>Member Functions</h3>
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<hr>
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<pre>
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adjacency_matrix(vertices_size_type n,
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const GraphProperty& p = GraphProperty())
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</pre>
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Creates a graph object with <tt>n</tt> vertices and zero edges.<br>
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(Required by <a href="MutableGraph.html">MutableGraph</a>.)
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<hr>
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<pre>
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template <typename EdgeIterator>
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adjacency_matrix(EdgeIterator first,
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EdgeIterator last,
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vertices_size_type n,
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const GraphProperty& p = GraphProperty())
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</pre>
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Creates a graph object with <tt>n</tt> vertices with the edges
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specified in the edge list given by the range <tt>[first, last)</tt>.
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The value type of the <tt>EdgeIterator</tt> must be a
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<tt>std::pair</tt>, where the type in the pair is an integer type. The
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integers will correspond to vertices, and they must all fall in the
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range of
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<tt>[0, n)</tt>. <br>
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(Required by <a href="IteratorConstructibleGraph.html">IteratorConstructibleGraph</a>.)
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<hr>
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<pre>
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template <typename EdgeIterator, typename EdgePropertyIterator>
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adjacency_matrix(EdgeIterator first, EdgeIterator last,
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EdgePropertyIterator ep_iter,
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vertices_size_type n,
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const GraphProperty& p = GraphProperty())
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</pre>
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Creates a graph object with <tt>n</tt> vertices, with the edges
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specified in the edge list given by the range <tt>[first, last)</tt>.
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The value type of the <tt>EdgeIterator</tt> must be a
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<tt>std::pair</tt>, where the type in the pair is an integer type. The
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integers will correspond to vertices, and they must all fall in the
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range of <tt>[0, n)</tt>. The <tt>value_type</tt> of the
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<tt>ep_iter</tt> should be <tt>EdgeProperty</tt>.
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<hr>
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<h3>Non-Member Functions</h3>
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<hr>
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<pre>
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std::pair<vertex_iterator, vertex_iterator>
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vertices(const adjacency_matrix& g)
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</pre>
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Returns an iterator-range providing access to the vertex set of graph <tt>g</tt>.<br>
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(Required by <a href="VertexListGraph.html">VertexListGraph</a>.)
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<hr>
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<pre>
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std::pair<edge_iterator, edge_iterator>
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edges(const adjacency_matrix& g);
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</pre>
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Returns an iterator-range providing access to the edge set of graph <tt>g</tt>.<br>
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(Required by <a href="EdgeListGraph.html">EdgeListGraph</a>.)
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<hr>
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<pre>
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std::pair<adjacency_iterator, adjacency_iterator>
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adjacent_vertices(vertex_descriptor v, const adjacency_matrix& g)
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</pre>
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Returns an iterator-range providing access to the vertices adjacent to
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vertex <tt>v</tt> in graph <tt>g</tt>.<br>
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(Required by <a href="AdjacencyGraph.html">AdjacencyGraph</a>.)
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<hr>
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<pre>
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std::pair<out_edge_iterator, out_edge_iterator>
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out_edges(vertex_descriptor v, const adjacency_matrix& g)
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</pre>
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Returns an iterator-range providing access to the out-edges of
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vertex <tt>v</tt> in graph <tt>g</tt>. If the graph is undirected,
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this iterator-range provides access to all edges incident on
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vertex <tt>v</tt>. <br>
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(Required by <a href="IncidenceGraph.html">IncidenceGraph</a>.)
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<hr>
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<pre>
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vertex_descriptor
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source(edge_descriptor e, const adjacency_matrix& g)
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</pre>
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Returns the source vertex of edge <tt>e</tt>.<br>
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(Required by <a href="IncidenceGraph.html">IncidenceGraph</a>.)
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<hr>
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<pre>
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vertex_descriptor
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target(edge_descriptor e, const adjacency_matrix& g)
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</pre>
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Returns the target vertex of edge <tt>e</tt>.<br>
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(Required by <a href="IncidenceGraph.html">IncidenceGraph</a>.)
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<hr>
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<pre>
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degree_size_type
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out_degree(vertex_descriptor u, const adjacency_matrix& g)
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</pre>
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Returns the number of edges leaving vertex <tt>u</tt>.<br>
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(Required by <a href="IncidenceGraph.html">IncidenceGraph</a>.)
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<hr>
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<hr>
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<pre>
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std::pair<in_edge_iterator, in_edge_iterator>
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in_edges(vertex_descriptor v, const adjacency_matrix& g)
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</pre>
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Returns an iterator-range providing access to the in-edges of
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vertex <tt>v</tt> in graph <tt>g</tt>. If the graph is undirected,
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this iterator-range provides access to all edges incident on
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vertex <tt>v</tt>. <br>
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(Required by <a href="BidirectionalGraph.html">BidirectionalGraph</a>.)
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<hr>
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<pre>
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degree_size_type
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in_degree(vertex_descriptor u, const adjacency_matrix& g)
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</pre>
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Returns the number of edges entering vertex <tt>u</tt>.<br>
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(Required by <a href="BidirectionalGraph.html">BidirectionalGraph</a>.)
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<hr>
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<hr>
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<pre>
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vertices_size_type num_vertices(const adjacency_matrix& g)
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</pre>
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Returns the number of vertices in the graph <tt>g</tt>.<br>
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(Required by <a href="VertexListGraph.html">VertexListGraph</a>.)
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<hr>
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<pre>
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edges_size_type num_edges(const adjacency_matrix& g)
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</pre>
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Returns the number of edges in the graph <tt>g</tt>.<br>
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(Required by <a href="EdgeListGraph.html">EdgeListGraph</a>.)
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<hr>
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<pre>
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vertex_descriptor vertex(vertices_size_type n, const adjacency_matrix& g)
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</pre>
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Returns the nth vertex in the graph's vertex list.
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<hr>
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<pre>
|
|
std::pair<edge_descriptor, bool>
|
|
edge(vertex_descriptor u, vertex_descriptor v,
|
|
const adjacency_matrix& g)
|
|
</pre>
|
|
Returns the edge connecting vertex <tt>u</tt> to vertex <tt>v</tt> in graph <tt>g</tt>.<br>
|
|
(Required by <a href="AdjacencyMatrix.html">AdjacencyMatrix</a>.)
|
|
|
|
<hr>
|
|
<pre>
|
|
std::pair<edge_descriptor, bool>
|
|
add_edge(vertex_descriptor u, vertex_descriptor v,
|
|
adjacency_matrix& g)
|
|
</pre>
|
|
Adds edge <tt>(u,v)</tt> to the graph and 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 <tt>bool</tt> flag will be <tt>false</tt>.
|
|
This operation does not invalidate any of the graph's iterators
|
|
or descriptors.<br>
|
|
(Required by <a href="MutableGraph.html">MutableGraph</a>.)
|
|
|
|
<hr>
|
|
<pre>
|
|
std::pair<edge_descriptor, bool>
|
|
add_edge(vertex_descriptor u, vertex_descriptor v,
|
|
const EdgeProperty& p,
|
|
adjacency_matrix& g)
|
|
</pre>
|
|
Adds edge <tt>(u,v)</tt> 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, vertex_descriptor v,
|
|
adjacency_matrix& g)
|
|
</pre>
|
|
Removes the edge <tt>(u,v)</tt> from the graph. <br>
|
|
(Required by <a href="MutableGraph.html">MutableGraph</a>.)
|
|
|
|
<hr>
|
|
<pre>
|
|
void remove_edge(edge_descriptor e, adjacency_matrix& g)
|
|
</pre>
|
|
Removes the edge <tt>e</tt> from the graph. This is equivalent
|
|
to calling <tt>remove_edge(source(e, g), target(e, g), g)</tt>.<br>
|
|
(Required by <a href="MutableGraph.html">MutableGraph</a>.)
|
|
|
|
<hr>
|
|
<pre>
|
|
void clear_vertex(vertex_descriptor u, adjacency_matrix& g)
|
|
</pre>
|
|
Removes all edges to and from vertex <tt>u</tt>. The vertex still appears
|
|
in the vertex set of the graph.<br>
|
|
(Required by <a href="MutableGraph.html">MutableGraph</a>.)
|
|
|
|
<hr>
|
|
<pre>
|
|
template <typename Property>
|
|
property_map<adjacency_matrix, Property>::type
|
|
get(Property, adjacency_matrix& g)
|
|
|
|
template <typename Property>
|
|
property_map<adjacency_matrix, Property>::const_type
|
|
get(Property, const adjacency_matrix& g)
|
|
</pre>
|
|
Returns the property map object for the vertex property specified by
|
|
<tt>Property</tt>. The <tt>Property</tt> must match one of the
|
|
properties specified in the graph's <tt>VertexProperty</tt> template
|
|
argument.<br>
|
|
(Required by <a href="PropertyGraph.html">PropertyGraph</a>.)
|
|
|
|
<hr>
|
|
<pre>
|
|
template <typename Property, typename X>
|
|
typename property_traits<
|
|
typename property_map<adjacency_matrix, Property>::const_type
|
|
>::value_type
|
|
get(Property, const adjacency_matrix& g, X x)
|
|
</pre>
|
|
This returns the property value for <tt>x</tt>, which is either
|
|
a vertex or edge descriptor.<br>
|
|
(Required by <a href="PropertyGraph.html">PropertyGraph</a>.)
|
|
|
|
<hr>
|
|
<pre>
|
|
template <typename Property, typename X, typename Value>
|
|
void
|
|
put(Property, const adjacency_matrix& 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<property_map<adjacency_matrix, Property>::type>::value_type</tt>.<br>
|
|
(Required by <a href="PropertyGraph.html">PropertyGraph</a>.)
|
|
|
|
<hr>
|
|
<pre>
|
|
template <typename GraphProperty, typename GraphProperty>
|
|
typename property_value<GraphProperty, GraphProperty>::type&
|
|
get_property(adjacency_matrix& g, GraphProperty)
|
|
</pre>
|
|
Return the property specified by <tt>GraphProperty</tt> that is attached
|
|
to the graph object <tt>g</tt>. The <tt>property_value</tt> traits class
|
|
is defined in <tt>boost/pending/property.hpp</tt>.
|
|
|
|
<hr>
|
|
<pre>
|
|
template <typename GraphProperty, typename GraphProperty>
|
|
const typename property_value<GraphProperty, GraphProperty>::type&
|
|
get_property(const adjacency_matrix& g, GraphProperty)
|
|
</pre>
|
|
Return the property specified by <tt>GraphProperty</tt> that is
|
|
attached to the graph object <tt>g</tt>. The <tt>property_value</tt>
|
|
traits class is defined in <tt>boost/pending/property.hpp</tt>.
|
|
|
|
|
|
<hr>
|