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<ul class="md-nav__list">
<li class="md-nav__item">
<a href="#_1" class="md-nav__link">
邻接矩阵
<a href="#1" class="md-nav__link">
1. &nbsp; 邻接矩阵
</a>
</li>
<li class="md-nav__item">
<a href="#_2" class="md-nav__link">
邻接表
<a href="#2" class="md-nav__link">
2. &nbsp; 邻接表
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</li>
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<ul class="md-nav__list">
<li class="md-nav__item">
<a href="#_1" class="md-nav__link">
邻接矩阵
<a href="#1" class="md-nav__link">
1. &nbsp; 邻接矩阵
</a>
</li>
<li class="md-nav__item">
<a href="#_2" class="md-nav__link">
邻接表
<a href="#2" class="md-nav__link">
2. &nbsp; 邻接表
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</ul>
<h2 id="913">9.1.3 &nbsp; 图的表示<a class="headerlink" href="#913" title="Permanent link">&para;</a></h2>
<p>图的常用表示方法包括「邻接矩阵」和「邻接表」。以下使用无向图进行举例。</p>
<h3 id="_1">邻接矩阵<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h3>
<h3 id="1">1. &nbsp; 邻接矩阵<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
<p>设图的顶点数量为 <span class="arithmatex">\(n\)</span> ，「邻接矩阵 Adjacency Matrix」使用一个 <span class="arithmatex">\(n \times n\)</span> 大小的矩阵来表示图，每一行（列）代表一个顶点，矩阵元素代表边，用 <span class="arithmatex">\(1\)</span> 或 <span class="arithmatex">\(0\)</span> 表示两个顶点之间是否存在边。</p>
<p>如下图所示，设邻接矩阵为 <span class="arithmatex">\(M\)</span> 、顶点列表为 <span class="arithmatex">\(V\)</span> ，那么矩阵元素 <span class="arithmatex">\(M[i][j] = 1\)</span> 表示顶点 <span class="arithmatex">\(V[i]\)</span> 到顶点 <span class="arithmatex">\(V[j]\)</span> 之间存在边，反之 <span class="arithmatex">\(M[i][j] = 0\)</span> 表示两顶点之间无边。</p>
<p><img alt="图的邻接矩阵表示" src="../graph.assets/adjacency_matrix.png" /></p>
@@ -3534,7 +3534,7 @@ G &amp; = \{ V, E \} \newline
<li>将邻接矩阵的元素从 <span class="arithmatex">\(1\)</span> , <span class="arithmatex">\(0\)</span> 替换为权重，则可表示有权图。</li>
</ul>
<p>使用邻接矩阵表示图时，我们可以直接访问矩阵元素以获取边，因此增删查操作的效率很高，时间复杂度均为 <span class="arithmatex">\(O(1)\)</span> 。然而，矩阵的空间复杂度为 <span class="arithmatex">\(O(n^2)\)</span> ，内存占用较多。</p>
<h3 id="_2">邻接表<a class="headerlink" href="#_2" title="Permanent link">&para;</a></h3>
<h3 id="2">2. &nbsp; 邻接表<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
<p>「邻接表 Adjacency List」使用 <span class="arithmatex">\(n\)</span> 个链表来表示图，链表节点表示顶点。第 <span class="arithmatex">\(i\)</span> 条链表对应顶点 <span class="arithmatex">\(i\)</span> ，其中存储了该顶点的所有邻接顶点（即与该顶点相连的顶点）。</p>
<p><img alt="图的邻接表表示" src="../graph.assets/adjacency_list.png" /></p>
<p align="center"> 图：图的邻接表表示 </p>