From the webpage:
Database of interesting graphs
Most graph theorists will agree that among the vast number of graphs that exist there are only a few that can be considered really interesting.
It is the aim of this House of Graphs project to find a workable definition of ‘interesting’ and provide a searchable database of graphs that conform to this definition. And to allow users to add additional graphs which they find interesting. In order to avoid abuse, only registered users can add new graphs.
Be sure to check out the Graph meta-directory for lists of graphs and graph generators.
A deeper understanding of graphs will serve you well, whatever graph solution you choose.