We derive a simple analytical line integral expression for the relaxation volume tensor of an arbitrary interconnected dislocation network. This quantity determines the magnitude of dislocation contribution to the dimensional changes and volumetric swelling of a material, and highlights the fundamental dual role of dislocations as sources of internal strain as well as carriers of plastic deformation. To illustrate applications of the method, we compute the relaxation volume of a stacking fault tetrahedron, a defect commonly occurring in fcc metals; the volume of an unusual tetrahedral configuration formed by the (a/2)<111> and <001> dislocations in a bcc metal; and estimate the relative contribution of extended dislocations to the volume relaxation of heavily irradiated tungsten.