The pic shows we have a weed we can't identify. We think it uses runners and has a root system which promotes more and more weeds. When it grows enough there is a cluster of little purple flowers.

The weed gets everywhere and is a real nuisance. Do you know what this plant is? And lastly is there a way to eradicate this weed it's seems indestructible. Click Pics for larger views....

If you could please let us know where you are city/country that will help to narrow down the possibilities for this question.

We live in New York State (United States), just about at the southern edge of the Adirondack Park, near Lake George. About 50 Miles north of Albany, New York.

It looks like vetch, possibly Vicia villosa:

Hairy Vetch (Vicia villosa)

Looks like vetch to me also, but no guess as to species.

Yes, a Vetch.

Does any one have a tip for how to get rid of this stuff?

Put on rubber gloves, take 2 small sponges and soak up some weed killer and sandwich the vines with that, make sure not to touch any other plants. You can also put sponge soaked on the end of a pole and go around yard and spot kill. I do this as previous owners fed finches thistle, ouch...