Time is tight, so i cant work up an example today, but...
Strands are all associated with a particle. So, one aspect of your challenge is to create a progressive growth of particles at vertices... This has been widely done in a number of ways, there should be a couple of examples on my blog and elsewhere. Then, when a particle is formed at a vertex, you need to "grow" your strand down the edges to neighboring vertices. Again, this is well covered elsewhere, for instance check out polynoid guru Fabian Pross's blog "Monophyl."
Also some digging on my blog should reveal compounds which create linear strands to a pointPosition, or which build position arrays which can be used for same... You can make such a strand "grow" by either culling "n" points off the end of a strand and animating the number culled or by simply making your "target" endpoint the result of a linear interpolation between self pointPosition and neighboring vertex pointPosition, and animating the blend. You can alternatively simply multiply the vector by a scalar to increase/decrease its length which is how I created sketch-like "construction lines" in the video below.
This is a broad description I know, but this kind of approach works. Here is a viewport capture of some lookdev that took about 4 hours start to finish to make and which could have been (but wasnt) greatly extended from there...
http://www.vimeo.com/30688549 ...in this case the mesh was reasonably dense, so I also animated individual strand opacities via underlying weight maps (instead of creating particles over time, creating them all at once and then revealing them over time. If you are using Eric's "tagging," perhaps use the tags to determine opacity?)
Sorry for the rushed explanation, time is short, but give it a whirl I've done it in the past and it wasn't hard at all. Cheers
(Also cloud-guru tekano

did some very nice lookdev on a job we briefly shared where he used some of Eric's tools to make strand trails grow along edges, for a less mechanical, more organic look which was pretty cool, check his Vimeo posts he may have an example up?)