This query has been added in https://trac.sagemath.org/ticket/10433.
I don't think that priority queue can be of any help to speed up the 
current code.

On Sunday, April 10, 2022 at 11:03:41 AM UTC+2 adarsh.k...@gmail.com wrote:

> Hi everyone,
>
> I was going through Sage's codebase, and I came across the file
> ```
> SAGE_ROOT/src/sage/graphs/spanning_tree.pyx
> ```
> [image: Screenshot from 2022-04-10 14-27-45.png]
>
> In the TODO section, it is mentioned that 
> ```
>     - Rewrite: func:`kruskal` to use priority queues.
> ```
>
> I looked it up on Google and StackOverFlow, but I didn't come across any 
> such implementation. The standard implementations all prefer to use the 
> DisjointSet data structure. I would like to contribute to Sage and if 
> someone can point me to a good resource which discusses this concept, 
> preferably with a better time complexity than by using Disjoint Sets, that 
> would be really great
>

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