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<b>Data Structures and Algorithms 
with Object-Oriented Design Patterns in C++</b><br>
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<H1><A NAME="SECTION0017200000000000000000">Implementing Graphs</A></H1>
<P>
In keeping with the design framework used throughout this text,
we view graphs as specialized containers.
Formally, the graph  <IMG WIDTH=72 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline71355" SRC="img2282.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img2282.gif"  > is an ordered pair
comprised of two sets--a set of vertices and a set of edges.
Informally, we can view a graph as a container with two compartments,
one which holds vertices and one which holds edges.
Therefore, there are three kinds of objects--vertices, edges, and graphs.
Accordingly, we need three object classes:
<tt>Vertex</tt>, <tt>Edge</tt>, and <tt>Graph</tt>.
(See Figure&nbsp;<A HREF="page536.html#figclasses9" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page536.html#figclasses9"><IMG  ALIGN=BOTTOM ALT="gif" SRC="cross_ref_motif.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/icons/cross_ref_motif.gif"></A>).
<P>
<P><A NAME="49674">&#160;</A><A NAME="figclasses9">&#160;</A> <IMG WIDTH=575 HEIGHT=174 ALIGN=BOTTOM ALT="figure49670" SRC="img2372.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img2372.gif"  ><BR>
<STRONG>Figure:</STRONG> Object Class Hierarchy<BR>
<P><BR> <HR>
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<LI> <A NAME="tex2html8540" HREF="page537.html#SECTION0017210000000000000000" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page537.html#SECTION0017210000000000000000">Implementing Vertices</A>
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<LI> <A NAME="tex2html8544" HREF="page546.html#SECTION0017250000000000000000" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page546.html#SECTION0017250000000000000000">Edge-Weighted and Vertex-Weighted Graphs</A>
<LI> <A NAME="tex2html8545" HREF="page547.html#SECTION0017260000000000000000" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page547.html#SECTION0017260000000000000000">Comparison of Graph Representations</A>
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