To get new network analysis researchers started I recommend downloading a few of those really great collections of networks of all kind. Those have initially been collected here: http://forum.gephi.org/viewtopic.php?f=7&t=162

Twitter networks

See infochimps, they provide an excellent access to already existing Twitter networks.

You are also free to of course crawl your own twitter networks using my Twitterlyzer (Ruby on Rails framework) software or try Nodexl for beginners.

Social networks

Facebook networks

Financial networks

Biological networks

Semantic networks

A great collection of networks from the Konnect Project from University Koblenz

Konnect Project from University of Koblenz

A great collection of networks by Jure Laskovec in the SNAP Project

SNAP Project from U of Stanford

A third collection of standard social networks by people from the CASOS institute


A collection of mostly weighted and directed network data by Tore Opsahl

As part of his phd thesis Tore has collected quite a few weighted and directed networks




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