I have created a network which consists of number of vertexes and edges. How do I show a popup message over a vertex when I move the mouse to that vertex?
AbstractPopupGraphMousePlugin and its subclasses are what you want: http://jung.sourceforge.net/doc/api/edu/uci/ics/jung/visualization/control/AbstractPopupGraphMousePlugin.html
Look for its use in PluggableRendererDemo and in GraphEditorDemo. (Other samples also use it; those samples show how to create subclasses.)