There is a CLI command for demonstrating graph templates (useful for developing them):
icingacli graphite icinga2 config
It generates Icinga 2 config based on the present graph templates. With this config Icinga will (also) “monitor” dummy services yielding random perfdata as expected by the graph templates.
I. e.: If that Icinga is also writing to the Graphite that is read by your Icinga Web Graphite Integration, you’ll get dummy graphs for all templates.