Cytoscape Web is an open-source graph visualisation library for the web. It is written in JavaScript as a jQuery library.
Cytoscape Web allows you to easily display graphs in your websites. Because Cytoscape Web allows the user to interact with the graph and the library allows the client to hook into user events, Cytoscape Web is easily integrated into your webapp, especially since Cytoscape Web supports both desktop browsers, like Chrome, and iOS browsers, like on the iPad.
Cytoscape Web also has graph analysis in mind: The library contains a slew of useful functions in graph theory.