Thanks Thomas. Two things went wrong for me. Firstly, I expected the defaults to deal with such a question, and two I did anticipate a suffix with more than three characters.
In the end, I discovered, thanks to your prompt, that the filter stays as the last format chosen. Thus 'All Files' showed everything and stayed a the default opening choice. When I selected 'graphml' it stayed that way and opens all my saved graph files.
Thanks for the help.