I have used GraphStream recently for Processing data graphing projects, and it worked well.
Of course, the web crawling and parsing is a separate piece – and websites source code can very different today than it did in 2006. Honestly, if I was doing that today I might use Processing.py (which runs on JVM and can access GraphStream) and BeautifulSoup for the html parsing. But there are many, many options out there for web crawling, for html parsing, and for graph visualizing.