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<head><title>DirectedGraph -- a class for directed graphs</title>
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<div><h1>DirectedGraph -- a class for directed graphs</h1>
<div class="single"><h2>Description</h2>
<div><div>This class is a type of HashTable which represents directed graphs. It consists of a vertex set and a set of sequences (a,b) representing a directed edge from a to b.</div>
<table class="examples"><tr><td><pre>i1 : V = {a,b,c,d,e}; -- the vertex set</pre>
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<tr><td><pre>i2 : E = {(a,b),(b,c),(a,c),(a,d),(d,e)}; -- directed edges; (a,b) means a directed edge from a to b.</pre>
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<tr><td><pre>i3 : G = directedGraph(V,E)
o3 = DirectedGraph{cache => CacheTable }
DirectedEdges => {(a, b), (b, c), (a, c), (a, d), (d, e)}
Vertices => {a, b, c, d, e}
o3 : DirectedGraph</pre>
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<tr><td><pre>i4 : allPairsShortestPath(G)
o4 = | 0 1 1 1 2 |
| infinity 0 1 infinity infinity |
| infinity infinity 0 infinity infinity |
| infinity infinity infinity 0 1 |
| infinity infinity infinity infinity 0 |
5 5
o4 : Matrix RR <--- RR
53 53</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_directed__Graph.html" title="creating a directed graph">directedGraph</a> -- creating a directed graph</span></li>
<li><span><a href="___Vertices.html" title="the set of vertices a directed graph">Vertices</a> -- the set of vertices a directed graph</span></li>
<li><span><a href="___Directed__Edges.html" title="the set of directed edges of a directed graph">DirectedEdges</a> -- the set of directed edges of a directed graph</span></li>
<li><span><a href="_adjacency__Matrix.html" title="returns adjacency matrix of a directed graph">adjacencyMatrix</a> -- returns adjacency matrix of a directed graph</span></li>
<li><span><a href="_all__Pairs__Shortest__Path.html" title="computes lengths of shortest paths between all pairs in a directed graph">allPairsShortestPath</a> -- computes lengths of shortest paths between all pairs in a directed graph</span></li>
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<div class="waystouse"><h2>Methods that use an object of class DirectedGraph :</h2>
<ul><li><span>adjacencyMatrix(DirectedGraph), see <span><a href="_adjacency__Matrix.html" title="returns adjacency matrix of a directed graph">adjacencyMatrix</a> -- returns adjacency matrix of a directed graph</span></span></li>
<li><span>allPairsShortestPath(DirectedGraph), see <span><a href="_all__Pairs__Shortest__Path.html" title="computes lengths of shortest paths between all pairs in a directed graph">allPairsShortestPath</a> -- computes lengths of shortest paths between all pairs in a directed graph</span></span></li>
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<div class="waystouse"><h2>For the programmer</h2>
<p>The object <a href="___Directed__Graph.html" title="a class for directed graphs">DirectedGraph</a> is <span>a <a href="../../Macaulay2Doc/html/___Type.html">type</a></span>, with ancestor classes <a href="../../Macaulay2Doc/html/___Hash__Table.html" title="the class of all hash tables">HashTable</a> < <a href="../../Macaulay2Doc/html/___Thing.html" title="the class of all things">Thing</a>.</p>
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