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<H1>directed graph</H1>
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(data structure)

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<strong>Definition:</strong>
A <a href="graph.html" tppabs="http://hissa.nist.gov/dads/HTML/graph.html"><em>graph</em></a> whose <a href="edge.html" tppabs="http://hissa.nist.gov/dads/HTML/edge.html"><em>edges</em></a> are <em>ordered</em> pairs of  <a href="vertex.html" tppabs="http://hissa.nist.gov/dads/HTML/vertex.html"><em>vertices</em></a>.  That is, each edge goes from one vertex to another, rather than merely connecting the vertices.  Also known as "digraph."
<P><strong>See also</strong>
<a href="diracygraf.html" tppabs="http://hissa.nist.gov/dads/HTML/diracygraf.html"><em>directed acyclic graph</em></a>, <a href="undirectgraf.html" tppabs="http://hissa.nist.gov/dads/HTML/undirectgraf.html"><em>undirected graph</em></a>, <a href="hypergraph.html" tppabs="http://hissa.nist.gov/dads/HTML/hypergraph.html"><em>hypergraph</em></a>, <a href="multigraph.html" tppabs="http://hissa.nist.gov/dads/HTML/multigraph.html"><em>multigraph</em></a>.
<P><em>Note:
John N. Warfield &lt;Jnwarfield@aol.com&gt; provides the following history of directed graphs. <P> In the Harvard-Oxford books on Aristotle, one of the translators suggests that Aristotle actually used something akin to digraphs in his teachings, but  this was pure speculation. <P> Augustus De Morgan invented the Theory of Relations and  published the key work in 1847 -- the same year in which Boole published his  key book in which he credited De Morgan for essentially teaching Boole about  logic. <P> Since the Theory of Relations offers essentially the algebraic form of the  digraph, it is unlikely that there was any formal use before 1847. <P> Charles Sanders Peirce made clear the use of structural patterns in doing  basic work, but his own graphics were not very useful in extended form,  though some modern enthusiasts have extolled his "existential graphs". <P> The earliest actual drawing of a digraph as connected to De Morgan that I  have been able to find occurs in the 1919 book by Bertrand Russell titled  "Introduction to Mathematical Philosophy". <P> The best modern reference is the book by Harary, Norman, and Cartwright (1966?) titled "Structural Modeling--The Theory of Directed Graphs".</em>
<P>Author: <a href="terms.html#authorPEB" tppabs="http://hissa.nist.gov/dads/terms.html#authorPEB">PEB</a>

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Entry modified Thu Sep 30 10:04:07 1999.<BR>
HTML page formatted Wed Dec 22 09:35:10 1999.

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