While waiting yWorks to implement the .graphml association you can you the script below to do it yourself. Save and run the script from you yEd installation directory root.
The code below is also in Gist:
#! /bin/bash
# Run the script in the root of yEd installation directory
# Tested with Ubuntu 18.04
# Create a new mime type definition file
cat >graphml+xml-mime.xml << EOL
<?xml version="1.0"?>
<mime-type type="application/x-graphml+xml">
<comment>yEd graphml file (xml format)</comment>
<glob pattern="*.graphml"/>
<generic-icon name="x-application-graphml+xml"/>
</mime-type>
</mime-info>
EOL
# Install the new mime definition
sudo xdg-mime install graphml+xml-mime.xml
# Install icon (size 48 can be extracted from i4j_extf_2_1aawyej_k3n8ea.ico file)
sudo xdg-icon-resource install --context mimetypes --size 32 .install4j/yEd.png x-application-graphml+xml
# Append %F to yEd .desktop file so it is visible in "Open With Other Application" menu
sed -i '/Exec/ s/$/ %F/' ~/.local/share/applications/yEd\ Graph\ Editor-0.desktop
# Finally go to file manager, right click, select "Open With Other Application",
# click "View All Applications" and select yEd.