My wife and I recently moved into a new place near Austin, TX, and we have some serious work to do to get the yard in good shape. The url at the bottom of this post has pictures of a weed that has nearly taken over our entire backyard.

The yard is mostly St. Augustine mixed with this weed, which has an extensive branching network of low-lying vines like the ones seen in the pics. There are also some very thick roots at certain nodes in the branching network, which I have also included in the pictures.

If anyone can help me identify what this weed is and how to eliminate it, I would greatly appreciate it. Thanks in advance.

Here is a link that might be useful: vine-like weed