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📄 ds7.1.2.htm

📁 这是清华大学所用的数据结构的电子版教材
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<title>第一章&nbsp; 绪论</title>
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<p align="center"><span style="mso-bidi-font-size: 10.0pt; font-family: 宋体; mso-ascii-font-family: Times New Roman; mso-hansi-font-family: Times New Roman; mso-bidi-font-family: Times New Roman; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA"><b><font color="#FFFF00" size="6">图的相关术语</font></b></span></p>
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    <!--msthemelist--><td valign="baseline" width="42"><img src="expbul1a.gif" width="15" height="15" hspace="13"></td>
    <td valign="top" width="100%"><!--mstheme--><font face="宋体">
      <p class="MsoNormal"><b><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;mso-hansi-font-family:
&quot;Times New Roman&quot;"><font size="5" color="#FFFF00">无向图</font><font size="5" color="#FFFFFF">:在一个图中，如果任意两个顶点构成的偶对（</font></span><font size="5" color="#FFFFFF"><span lang="EN-US">vi, 
      vj</span><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;mso-hansi-font-family:
&quot;Times New Roman&quot;">）∈</span><span lang="EN-US">E</span><span style="font-family:
宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;mso-hansi-font-family:&quot;Times New Roman&quot;">是无序的，即顶点之间的连线是没有方向的，则称该图为无向图。如图</span><span lang="EN-US">8.1</span><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;
mso-hansi-font-family:&quot;Times New Roman&quot;">所示是一个无向图</span><span lang="EN-US">G1</span><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;mso-hansi-font-family:
&quot;Times New Roman&quot;">。</span></font></b><!--mstheme--></font><!--msthemelist--></td>
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    <!--msthemelist--><td valign="baseline" width="42"><img src="expbul1a.gif" width="15" height="15" hspace="13"></td>
    <td valign="top" width="100%"><!--mstheme--><font face="宋体">
      <p class="MsoNormal"><b><span style="font-family:
宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;mso-hansi-font-family:&quot;Times New Roman&quot;"><font size="5" color="#FFFF00">有向图</font><font size="5" color="#FFFFFF">:在一个图中，如果任意两个顶点构成的偶对（</font></span><font size="5" color="#FFFFFF"><span lang="EN-US">vi, 
      vj</span><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;
mso-hansi-font-family:&quot;Times New Roman&quot;">）∈</span><span lang="EN-US">E</span><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;mso-hansi-font-family:
&quot;Times New Roman&quot;">是有序的，即顶点之间的连线是有方向的，则称该图为有向图。如图</span><span lang="EN-US">8.2</span><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;mso-hansi-font-family:
&quot;Times New Roman&quot;">所示是一个有向图</span><span lang="EN-US">G2</span><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;mso-hansi-font-family:
&quot;Times New Roman&quot;">：</span></font></b><!--mstheme--></font><!--msthemelist--></td>
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<p class="MsoNormal" style="margin-top: 0; margin-bottom: 0"><span lang="EN-US"><b><font size="5" color="#FFFFFF"><span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
</span>G2=(V2,E2)</font></b></span></p>
<p class="MsoNormal" style="margin-top: 0; margin-bottom: 0"><span lang="EN-US"><span style="mso-spacerun:
yes"><font size="5" color="#FFFFFF"><b>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
</b></font></span><font size="5" color="#FFFFFF"><b>V2={v1,v2,v3,v4}</b></font></span></p>
<p class="MsoNormal" style="margin-top: 0; margin-bottom: 0"><span lang="EN-US"><span style="mso-spacerun:
yes"><font size="5" color="#FFFFFF"><b>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
</b></font></span><font size="5" color="#FFFFFF"><b>E2={&lt;v1,v2&gt;,&lt;v1,v3&gt;,&lt;v3,v4&gt;,&lt;v4,v1&gt;}</b></font></span></p>
<p class="MsoNormal" style="margin-top: 0; margin-bottom: 0" align="center"><img border="0" src="ds7.1.2.gif" width="325" height="124"></p>
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<!--msthemelist--><table border="0" cellpadding="0" cellspacing="0" width="100%">
  <!--msthemelist--><tr>
    <!--msthemelist--><td valign="baseline" width="42"><img src="expbul1a.gif" width="15" height="15" hspace="13"></td>
    <td valign="top" width="100%"><!--mstheme--><font face="宋体">
      <p class="MsoNormal"><b><span style="font-family:
宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;mso-hansi-font-family:&quot;Times New Roman&quot;"><font size="5" color="#FFFF00">顶点、边、弧、弧头、弧尾</font><font size="5" color="#FFFFFF">:图中，数据元素</font></span><font size="5" color="#FFFFFF"><span lang="EN-US">vi</span><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;
mso-hansi-font-family:&quot;Times New Roman&quot;">称为</span></font><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;
mso-hansi-font-family:&quot;Times New Roman&quot;"><font size="5" color="#FFFF00">顶点</font></span><font size="5" color="#FFFFFF"><span lang="EN-US">(vertex 
      )</span><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;mso-hansi-font-family:
&quot;Times New Roman&quot;">；</span><span lang="EN-US">P(vi, vj)</span><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;mso-hansi-font-family:
&quot;Times New Roman&quot;">表示在顶点</span><span lang="EN-US">vi</span><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;mso-hansi-font-family:
&quot;Times New Roman&quot;">和顶点</span><span lang="EN-US">vj</span><span style="font-family:
宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;mso-hansi-font-family:&quot;Times New Roman&quot;">之间有一条直接连线。如果是在无向图中，则称这条连线为</font><font size="5" color="#FFFF00">边</font><font size="5" color="#FFFFFF">；如果是在有向图中，一般称这条连线为</font><font size="5" color="#FFFF00">弧</font><font size="5" color="#FFFFFF">。边用顶点的无序偶对（</font></span><font size="5" color="#FFFFFF"><span lang="EN-US">vi, 
      vj</span><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;
mso-hansi-font-family:&quot;Times New Roman&quot;">）来表示，称顶点</span><span lang="EN-US">vi</span><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;mso-hansi-font-family:
&quot;Times New Roman&quot;">和顶点</span><span lang="EN-US">vj</span><span style="font-family:
宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;mso-hansi-font-family:&quot;Times New Roman&quot;">互为邻接点，边（</span><span lang="EN-US">vi, 
      vj</span><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;
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