Here you may find my random graph web application.
You may generate random graphs and trees by inputting parameters like graph density, minimum and maximum node degrees and number of nodes. The graphs are outputted in DIMACS format which I believe is easy to work with. So you may easily produce graphs for experimentation and software testing.
The most interesting part is the random tree generator. The algorithm that I have developed for it is interesting, I believe, and rather easy to understand. Considering the user inputted Graph Density parameter, for every node in the graph the algorithm decides whether or not to add adjoined nodes. This procedure is iterative until the graph reaches the desired number of nodes. The produced graph is a tree as every new node is adjoined only with one older node so circles may not be formed.
Why a web app?
I believe a web application is the best way to demonstrate a scientific idea, if it is possible to build an application about it. Web applications don’t need installation; they are easy to access; the user may easily get to the point of what they are all about.
The application is partially compatible with IE and Edge, you should better use it with Firefox or Chrome.