由于网页加载所有DOM组件需要一定的时间，所以也许您应该在脚本中包含一个window. onload事件函数，以便在页面第一次完全加载后调用graphUpdate（）函数：

window.onload = graphUpdate;

更多信息：https://developer.mozilla.org/en-US/docs/Web/API/Window/load_event
要保存所选值，可以使用window.localStorage，它允许您将值永久保存在浏览器中，因此事件函数可以如下所示：

window.onload = function() {
  // 1 by default, in case there is nothing saved
  let selected = window.localStorage.getItem('selectedGraph') || 1;
  document.querySelector('#selGraph').selectedIndex = selected;
  graphUpdate();
}

那么graphUpdate函数应该包含一行来存储值：

function graphUpdate(){
    let value = document.querySelector('#selGraph');
    let graph = ["graph_1.gv", "graph_2.gv", "graph_3.gv", "graph_4.gv", "graph_5.gv"]
    render(graph[value.selectedIndex]);
    window.localStorage.setItem('selectedGraph', value.selectedIndex)
}

链接：https://developer.mozilla.org/en-US/docs/Web/API/Window/localStorage

如果JS代码在文档元素存在之后运行（通过将<script>标记放在后面或使用defer），则可以简单地执行graphUpdate()函数。
要保存默认选项，我将使用localStorage。
最后，不建议使用基于属性的事件侦听器，如onchange和onclick。

<label for="alternativeGraph">Alternative graphs could be seen here:</label>
<select id="selGraph" aria-label="Graph">
  <!-- values are easier to work with than indexes -->
  <option value="graph_1.gv">Graph 1</option>
  <option value="graph_2.gv">Graph 2</option>
  <option value="graph_3.gv">Graph 3</option>
  <option value="graph_4.gv">Graph 4</option>
  <option value="graph_5.gv">Graph 5</option>
</select>
<button type="button" id="setDefaultGraphBtn">Change default graph</button>

// Constants
const DEFAULT_GRAPH_KEY = "default-graph";
const DEFAULT_GRAPH = "graph_1.gv";

// Elements
const graphSelect = document.getElementById("selGraph");
const btn = document.getElementById("setDefaultGraphBtn");

// Functions
const render = async (filename) => {
  const res = await fetch(filename);
  if (!res.ok) {
    throw new Error(`${filename}: ${res.status} ${res.statusText}`);
  }

  renderString(await res.text());
};

const graphUpdate = () => {
  render(graphSelect.value);
};

const setDefaultGraph = () => {
  const val = graphSelect.value;
  localStorage.setItem(DEFAULT_GRAPH_KEY, val);
  graphSelect.querySelectorAll("option").forEach((opt) => {
    // remove any previous "default" text
    opt.textContent = opt.textContent.replace(" (default)", "");
    // add "default" text
    if (opt.value === val) {
      opt.textContent += " (default)";
    }
  });
};

// Bind event listeners
graphSelect.addEventListener("change", graphUpdate);
btn.addEventListener("click", setDefaultGraph);

// Get localStorage value or default
const defaultGraph = localStorage.getItem(DEFAULT_GRAPH_KEY) ?? DEFAULT_GRAPH;

// set default selected
graphSelect.value = defaultGraph;

// Now run functions to initialise
setDefaultGraph();
graphUpdate();