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<HTML><HEAD><TITLE>Graph Traversal Applications: Testing for Cycles and Connectedness</TITLE></HEAD><BODY bgcolor="#FFFFFF"> <a href="../index.html" target="_top"><img src="../icons/usins.gif" alt="Logo" align=right></a><b>Data Structures and Algorithms with Object-Oriented Design Patterns in Python</b><br><A NAME="tex2html7571" HREF="page559.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="../icons/next_motif.gif"></A> <A NAME="tex2html7569" HREF="page548.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="../icons/up_motif.gif"></A> <A NAME="tex2html7565" HREF="page557.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="../icons/previous_motif.gif"></A> <A NAME="tex2html7573" HREF="page611.html"><IMG WIDTH=43 HEIGHT=24 ALIGN=BOTTOM ALT="index" SRC="../icons/index_motif.gif"></A> <BR><HR><H2><A NAME="SECTION0016340000000000000000">Graph Traversal Applications:<BR> Testing for Cycles and Connectedness</A></H2><P><A NAME="secgraphconnected"> </A><P>This section presents several graph algorithmsthat are based on graph traversals.The first two algorithms testundirected and directed graphs for connectedness.Both algorithms are implemented using the depth-first traversal.The third algorithm tests a directed graph for cycles.It is implemented using a topological-order traversal.<P><BR> <HR><UL> <LI> <A NAME="tex2html7574" HREF="page559.html#SECTION0016341000000000000000">Connectedness of an Undirected Graph</A><LI> <A NAME="tex2html7575" HREF="page560.html#SECTION0016342000000000000000">Connectedness of a Directed Graph</A><LI> <A NAME="tex2html7576" HREF="page561.html#SECTION0016343000000000000000">Testing Strong Connectedness</A><LI> <A NAME="tex2html7577" HREF="page562.html#SECTION0016344000000000000000">Testing for Cycles in a Directed Graph</A></UL><HR><A NAME="tex2html7571" HREF="page559.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="../icons/next_motif.gif"></A> <A NAME="tex2html7569" HREF="page548.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="../icons/up_motif.gif"></A> <A NAME="tex2html7565" HREF="page557.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="../icons/previous_motif.gif"></A> <A NAME="tex2html7573" HREF="page611.html"><IMG WIDTH=43 HEIGHT=24 ALIGN=BOTTOM ALT="index" SRC="../icons/index_motif.gif"></A> <P><ADDRESS><img src="../icons/bruno.gif" alt="Bruno" align=right><a href="../copyright.html">Copyright © 2003</a> by <a href="../signature.html">Bruno R. Preiss, P.Eng.</a> All rights reserved.</ADDRESS></BODY></HTML>
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