I wrote a small Java tool to download my twitter network as a GEXF file. This tool is available on github at:
java -jar twittergraph.jar -o twittergraph.gexf 7431072 #my twitter ID
This tool doesn't use the OAuth API, so it have to wait for a few minutes, and retry to connect, every times it reaches the twitter API quotas (150 requests per hour). In the end it took one night to download the data from my network (~390 friends).
The GEXF file was then opened with Gephi, processed with the ForceAtlas algorithm and exported as a PDF file.
The PDF file was uploaded on scribd: http://www.scribd.com/doc/48415306/My-Twitter-Network
I then, downloaded the PDF from scribd.com, quickly copied the URL of the generated PDF and pasted it into http://zoom.it/.
Here is the result ! :-)
That's it !