I think this is going to be extremely computationally intensive. One of the big performance wins I got when designing the search algorithm[1] was visiting as few nodes in the graph as possible (which I did via a bi-directional breadth-first search). To find the most distant node, I'd need to traverse the entire graph, which consists of almost 6 million nodes. It can be done, but it would take minutes, hours, days, ...
[1] https://github.com/jwngr/sdow/blob/a2699dc95d884ec64a4641630...