The DynNetwork plugin for Cytoscape 3.x has an option for playing and recording. However, I never got it to work so in the end, I always export each time point as a png image, each image being named sequentially e.g. T01.png, T02.png,... then I used ffmpeg (or avconv on Ubuntu 14.x) to assemble them into a video, e.g.:

ffmpeg -framerate 1/2 -i T%02d.png video.mp4

See the ffmpeg docs here.

In case you wanted to also add a soundtrack (probably not recommended as it will be distracting but for fun):

ffmpeg -i video.mp4 -i star-wars-theme-song.mp3 -map 0:0 -map 1:0 -c:v copy -c:a copy output.mp4