We have a GEXF download option.

However, more streamlined would be to allow to display the graph directly.

I'm not sure about Gephi itself, but there's gephi-lite which allows for a ?gexf= querystring parameter.

E.g.:

https://gephi.org/gephi-lite/?gexf=https%3A%2F%2Fraw.githubusercontent.com%2Fgephi%2Fgephi.github.io%2Frefs%2Fheads%2Fmaster%2Fdatasets%2Fairlines-sample.gexf

would open the airlines-sample.gexf from github: https://github.com/gephi/gephi.github.io/blob/master/datasets/airlines-sample.gexf

We could add something simliar to the 'share url' option and directly open gephi-lite to the user's graph. If Gephi desktop supports loading remote files, we could allow the user to just copy the URL of the GEXF file, then paste that in Gephi window.