Parallel graphs were a starting point on multidimensional al visualization. They are useful only to a certain point of complexity, then they are counterproductive as it takes more time to analyze the graphs than to view a number of simpler graphs side by side or in series. Newer techniques involve radial visualization, such as
http://www.infovis-wiki.net/index.php?title=Radial_Hierarchi...
Something to consider with your animations is the cognitive load of animations of complex visualizations. See the following paper: