Cosmic strings, if they exist, would be extremely thin with diameters on the same order as a proton. They would have immense density, however, and so would represent significant gravitational sources. Cosmic strings would form a network of loops in the early universe, and their gravity could have been responsible for the original clumping of matter into galactic superclusters.
Cosmic strings pinch off small isolated loops of themselves, which decay via gravitational radiation.
Other types of topological defects in spacetime are domain walls, monopoles, and texturess.