[Vuejs]-Is there a way to detect when the actual DOM render completes?

I hate to suggest this but as a work around you can add a <script>...</script> snippet which triggers an event (soon before the EOF the Vue component) which you can handle to call your graph render function.
It should approximately look like this:

<vue-component> 
    <!-- component contents -->
    <!-- ... -->
    <script> // trigger-code </script> 
</vue-component>

Let me know if that works for you.

You can use a ref (see docs) to apply changes to the DOM.

Use it in the mounted hook in the same component that holds the <canvas> element.