katex公式报错[Bug]

[AndersonHJB]

Checklist

• I am using LTS version of Node.js.
• I am using the latest v2 version of VuePress and VuePress official plugins.
• I am using the latest v2 version of vuepress-theme-hope and all plugins in this repo.
• I followed the docs and I double checked my configuration.
• I have searched FAQ and I did not find the answer.

Package name

vuepress-theme-hope

Which operating system are you using?

• macOS
• Windows
• Linux

Describe the bug

当下面的Markdown文件放在网站中，主题中启动katex: true，会直接报错。
但是使用 mathjax: true,就不会报错，公式编写没有问题。报错推测 vite 和公式结合问题？

Assessed-coursework4.md
报错截图：

最小实现链接：https://github.com/BornforthisHJB/BornforthisHJB.github.io/tree/33fbcdaec5565038d04987efbb46603d4c41296b

Additional context

命令行输出结果：

7:39:41 AM [vite] Internal server error: Error parsing JavaScript expression: Unexpected token (1:1)
  Plugin: vite:vue
  File: /Users/huangjiabao/GitHub/StudentWebSite/MyWebSite/BornforthisHJB.github.io/src/.vuepress/.temp/pages/HomeWork/YuShu/Assessed-coursework4.html.vue:105:20242
  103|  <span class="token comment">## Delta : ['Beta', 'Delta']</span>
  104|  <span class="token comment">## Epsilon : ['Alpha', 'Delta']</span>
  105|  </code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><p>Recall that by default, the Graph class represents directed graphs. However, we can also use objects from this class to represent undirected graphs.Recall that for an undirected graph <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>G</mi><mo>=</mo><mo stretchy="false">(</mo><mi>V</mi><mo separator="true">,</mo><mi>E</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">G=(V,E)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">G</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.22222em;">V</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">E</span><span class="mclose">)</span></span></span></span> each edge <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>e</mi><mo>=</mo><mo stretchy="false">{</mo><mi>x</mi><mo separator="true">,</mo><mi>y</mi><mo stretchy="false">}</mo></mrow><annotation encoding="application/x-tex">e=\{x,y\}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">e</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">{</span><span class="mord mathnormal">x</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mclose">}</span></span></span></span> corresponds to a set of two distinct nodes <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi><mo separator="true">,</mo><mi>y</mi><mo>∈</mo><mi>V</mi></mrow><annotation encoding="application/x-tex">x,y \in V</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">x</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">∈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.22222em;">V</span></span></span></span> . Unlike directed graphs, for undirected graphs there is no ordering between the nodes for a specific edge. We can represent an undirected graph <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>G</mi><mo>=</mo><mo stretchy="false">(</mo><mi>V</mi><mo separator="true">,</mo><mi>E</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">G=(V,E)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">G</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.22222em;">V</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">E</span><span class="mclose">)</span></span></span></span> via an associated directed graph <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mi>G</mi><mo>~</mo></mover><mo>=</mo><mo stretchy="false">(</mo><mover accent="true"><mi>V</mi><mo>~</mo></mover><mo separator="true">,</mo><mover accent="true"><mi>E</mi><mo>~</mo></mover><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\tilde{G}=(\tilde{V}, \tilde{E})</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9202em;"></span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9202em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal">G</span></span><span style="top:-3.6023em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.1667em;"><span class="mord">~</span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.1702em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9202em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal" style="margin-right:0.22222em;">V</span></span><span style="top:-3.6023em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">~</span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9202em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">E</span></span><span style="top:-3.6023em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.1667em;"><span class="mord">~</span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span> with the same set of nodes <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mi>V</mi><mo>~</mo></mover><mo>=</mo><mi>V</mi></mrow><annotation encoding="application/x-tex">\tilde{V}=V</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9202em;"></span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9202em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal" style="margin-right:0.22222em;">V</span></span><span style="top:-3.6023em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">~</span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.22222em;">V</span></span></span></span> and for each undirected edge <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>e</mi><mo>=</mo><mo stretchy="false">{</mo><mi>x</mi><mo separator="true">,</mo><mi>y</mi><mo stretchy="false">}</mo><mo>=</mo><mo stretchy="false">{</mo><mi>y</mi><mo separator="true">,</mo><mi>x</mi><mo stretchy="false">}</mo><mo>∈</mo><mi>E</mi></mrow><annotation encoding="application/x-tex">e=\{x,y\}=\{y,x\} \in E</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">e</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">{</span><span class="mord mathnormal">x</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mclose">}</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">{</span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">x</span><span class="mclose">}</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">∈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">E</span></span></span></span> we include both of the corresponding directed edges <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mover accent="true"><mi>e</mi><mo>~</mo></mover><mn>0</mn></msub><mo>=</mo><mo stretchy="false">(</mo><mi>x</mi><mo separator="true">,</mo><mi>y</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\tilde{e}_0=(x,y)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8179em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6679em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal">e</span></span><span style="top:-3.35em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.1944em;"><span class="mord">~</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mclose">)</span></span></span></span> (from <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">x</span></span></span></span> to <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>y</mi></mrow><annotation encoding="application/x-tex">y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span></span></span></span>) and <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mover accent="true"><mi>e</mi><mo>~</mo></mover><mn>1</mn></msub><mo>=</mo><mo stretchy="false">(</mo><mi>y</mi><mo separator="true">,</mo><mi>x</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\tilde{e}_1=(y,x)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8179em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6679em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal">e</span></span><span style="top:-3.35em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.1944em;"><span class="mord">~</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">x</span><span class="mclose">)</span></span></span></span> (from <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>y</mi></mrow><annotation encoding="application/x-tex">y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span></span></span></span> to <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">x</span></span></span></span>) in the set <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mi>E</mi><mo>~</mo></mover></mrow><annotation encoding="application/x-tex">\tilde{E}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9202em;"></span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9202em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">E</span></span><span style="top:-3.6023em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.1667em;"><span class="mord">~</span></span></span></span></span></span></span></span></span></span>. As an example, consider an undirected graph <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>G</mi><mo>=</mo><mo stretchy="false">(</mo><mi>V</mi><mo separator="true">,</mo><mi>E</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">G=(V,E)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">G</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.22222em;">V</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">E</span><span class="mclose">)</span></span></span></span> with <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>V</mi><mo>=</mo><mo stretchy="false">{</mo><mi>a</mi><mo separator="true">,</mo><mi>b</mi><mo separator="true">,</mo><mi>c</mi><mo separator="true">,</mo><mi>d</mi><mo stretchy="false">}</mo></mrow><annotation encoding="application/x-tex">V=\{a,b,c,d\}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.22222em;">V</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">{</span><span class="mord mathnormal">a</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">b</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">c</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">d</span><span class="mclose">}</span></span></span></span> and <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>E</mi><mo>=</mo><mo stretchy="false">{</mo><mo stretchy="false">{</mo><mi>a</mi><mo separator="true">,</mo><mi>b</mi><mo stretchy="false">}</mo><mo separator="true">,</mo><mo stretchy="false">{</mo><mi>b</mi><mo separator="true">,</mo><mi>c</mi><mo stretchy="false">}</mo><mo separator="true">,</mo><mo stretchy="false">{</mo><mi>a</mi><mo separator="true">,</mo><mi>c</mi><mo stretchy="false">}</mo><mo stretchy="false">}</mo></mrow><annotation encoding="application/x-tex">E=\{\{a,b\},\{b,c\},\{a,c\}\}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">E</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">{{</span><span class="mord mathnormal">a</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">b</span><span class="mclose">}</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mopen">{</span><span class="mord mathnormal">b</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">c</span><span class="mclose">}</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mopen">{</span><span class="mord mathnormal">a</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">c</span><span class="mclose">}}</span></span></span></span>. We can represent <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>G</mi></mrow><annotation encoding="application/x-tex">G</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">G</span></span></span></span> via the directed graph <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mi>G</mi><mo>~</mo></mover><mo>=</mo><mo stretchy="false">(</mo><mover accent="true"><mi>V</mi><mo>~</mo></mover><mo separator="true">,</mo><mover accent="true"><mi>E</mi><mo>~</mo></mover><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\tilde{G}=(\tilde{V},\tilde{E})</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9202em;"></span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9202em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal">G</span></span><span style="top:-3.6023em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.1667em;"><span class="mord">~</span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.1702em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9202em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal" style="margin-right:0.22222em;">V</span></span><span style="top:-3.6023em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">~</span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9202em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">E</span></span><span style="top:-3.6023em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.1667em;"><span class="mord">~</span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span> where <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mi>V</mi><mo>~</mo></mover><mo>=</mo><mi>V</mi></mrow><annotation encoding="application/x-tex">\tilde{V}=V</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9202em;"></span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9202em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal" style="margin-right:0.22222em;">V</span></span><span style="top:-3.6023em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">~</span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.22222em;">V</span></span></span></span> and <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mi>E</mi><mo>~</mo></mover><mo>=</mo><mo stretchy="false">{</mo><mo stretchy="false">(</mo><mi>a</mi><mo separator="true">,</mo><mi>b</mi><mo stretchy="false">)</mo><mo separator="true">,</mo><mo stretchy="false">(</mo><mi>b</mi><mo separator="true">,</mo><mi>a</mi><mo stretchy="false">)</mo><mo separator="true">,</mo><mo stretchy="false">(</mo><mi>b</mi><mo separator="true">,</mo><mi>c</mi><mo stretchy="false">)</mo><mo separator="true">,</mo><mo stretchy="false">(</mo><mi>c</mi><mo separator="true">,</mo><mi>b</mi><mo stretchy="false">)</mo><mo separator="true">,</mo><mo stretchy="false">(</mo><mi>a</mi><mo separator="true">,</mo><mi>c</mi><mo stretchy="false">)</mo><mo separator="true">,</mo><mo stretchy="false">(</mo><mi>c</mi><mo separator="true">,</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">}</mo></mrow><annotation encoding="application/x-tex">\tilde{E}=\{(a,b),(b,a),(b,c),(c,b),(a,c),(c,a)\}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9202em;"></span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9202em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">E</span></span><span style="top:-3.6023em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.1667em;"><span class="mord">~</span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">{(</span><span class="mord mathnormal">a</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">b</span><span class="mclose">)</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mopen">(</span><span class="mord mathnormal">b</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">a</span><span class="mclose">)</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mopen">(</span><span class="mord mathnormal">b</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">c</span><span class="mclose">)</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mopen">(</span><span class="mord mathnormal">c</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">b</span><span class="mclose">)</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mopen">(</span><span class="mord mathnormal">a</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">c</span><span class="mclose">)</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mopen">(</span><span class="mord mathnormal">c</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">a</span><span class="mclose">)}</span></span></span></span>.Note that this representation doubles the number of edges. We use the adjacency list representation within the class Graph for the associated graph <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mi>G</mi><mo>~</mo></mover><mo>=</mo><mo stretchy="false">(</mo><mover accent="true"><mi>V</mi><mo>~</mo></mover><mo separator="true">,</mo><mover accent="true"><mi>E</mi><mo>~</mo></mover><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\tilde{G}=(\tilde{V},\tilde{E})</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9202em;"></span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9202em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal">G</span></span><span style="top:-3.6023em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.1667em;"><span class="mord">~</span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.1702em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9202em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal" style="margin-right:0.22222em;">V</span></span><span style="top:-3.6023em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">~</span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9202em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">E</span></span><span style="top:-3.6023em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.1667em;"><span class="mord">~</span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span> to represent the undirected graph <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>G</mi><mo>=</mo><mo stretchy="false">(</mo><mi>V</mi><mo separator="true">,</mo><mi>E</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">G=(V,E)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">G</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.22222em;">V</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">E</span><span class="mclose">)</span></span></span></span>.</p>
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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 ^
  106|  <p>Note that graphs of this form correspond to symmetric adjacency matrices with zeros along the diagonal (since there are no self-edges in an undirected graph). The following code can be used to create a random adjacency matrix of this form:</p>
  107|  <div class="language-python line-numbers-mode" data-ext="py"><pre v-pre class="language-python"><code><span class="token keyword">def</span> <span class="token function">generate_random_symmetric_matrix_zero_diagonal</span><span class="token punctuation">(</span>n<span class="token punctuation">:</span><span class="token builtin">int</span><span class="token punctuation">,</span> prob<span class="token punctuation">:</span><span class="token builtin">float</span><span class="token punctuation">)</span> <span class="token operator">-</span><span class="token operator">></span> np<span class="token punctuation">.</span>array<span class="token punctuation">:</span>
      at createCompilerError (/Users/huangjiabao/GitHub/StudentWebSite/MyWebSite/BornforthisHJB.github.io/node_modules/.pnpm/@vue+compiler-core@3.3.8/node_modules/@vue/compiler-core/dist/compiler-core.cjs.js:18:17)
      at processExpression (/Users/huangjiabao/GitHub/StudentWebSite/MyWebSite/BornforthisHJB.github.io/node_modules/.pnpm/@vue+compiler-core@3.3.8/node_modules/@vue/compiler-core/dist/compiler-core.cjs.js:3200:7)
      at Array.transformExpression (/Users/huangjiabao/GitHub/StudentWebSite/MyWebSite/BornforthisHJB.github.io/node_modules/.pnpm/@vue+compiler-core@3.3.8/node_modules/@vue/compiler-core/dist/compiler-core.cjs.js:3086:20)
      at traverseNode (/Users/huangjiabao/GitHub/StudentWebSite/MyWebSite/BornforthisHJB.github.io/node_modules/.pnpm/@vue+compiler-core@3.3.8/node_modules/@vue/compiler-core/dist/compiler-core.cjs.js:2018:38)
      at traverseChildren (/Users/huangjiabao/GitHub/StudentWebSite/MyWebSite/BornforthisHJB.github.io/node_modules/.pnpm/@vue+compiler-core@3.3.8/node_modules/@vue/compiler-core/dist/compiler-core.cjs.js:2010:5)
      at traverseNode (/Users/huangjiabao/GitHub/StudentWebSite/MyWebSite/BornforthisHJB.github.io/node_modules/.pnpm/@vue+compiler-core@3.3.8/node_modules/@vue/compiler-core/dist/compiler-core.cjs.js:2052:7)
      at traverseChildren (/Users/huangjiabao/GitHub/StudentWebSite/MyWebSite/BornforthisHJB.github.io/node_modules/.pnpm/@vue+compiler-core@3.3.8/node_modules/@vue/compiler-core/dist/compiler-core.cjs.js:2010:5)
      at traverseNode (/Users/huangjiabao/GitHub/StudentWebSite/MyWebSite/BornforthisHJB.github.io/node_modules/.pnpm/@vue+compiler-core@3.3.8/node_modules/@vue/compiler-core/dist/compiler-core.cjs.js:2052:7)
      at traverseChildren (/Users/huangjiabao/GitHub/StudentWebSite/MyWebSite/BornforthisHJB.github.io/node_modules/.pnpm/@vue+compiler-core@3.3.8/node_modules/@vue/compiler-core/dist/compiler-core.cjs.js:2010:5)
      at traverseNode (/Users/huangjiabao/GitHub/StudentWebSite/MyWebSite/BornforthisHJB.github.io/node_modules/.pnpm/@vue+compiler-core@3.3.8/node_modules/@vue/compiler-core/dist/compiler-core.cjs.js:2052:7)

[AndersonHJB]

一个额外的话题：icon 能否支持彩色的？

[Mister-Hope]

你最好搞一个真的最小复现。

[AndersonHJB]

你最好搞一个真的最小复现。

那个链接是真的，就一篇文章在里😂

https://github.com/BornforthisHJB/BornforthisHJB.github.io/tree/33fbcdaec5565038d04987efbb46603d4c41296b

[Mister-Hope]

你最好搞一个真的最小复现。

[github-actions]

Hello @AndersonHJB. Please provide a minimal reproduction using a GitHub repository or vuepress-theme-hope.github.io/v2-new. Issues marked with needs reproduction will be closed if they have no activity within 3 days.

[AndersonHJB]

https://stackblitz.com/edit/vuepress-theme-hope-3nr5aq?file=docs%2FREADME.md

[Mister-Hope]

That's still not a minimal reproduction, I want just a few lines of markdown which can let to the issue.

[AndersonHJB]

https://stackblitz.com/edit/vuepress-theme-hope-3nr5aq?file=docs%2FREADME.md