We show that using a density-functional supercell method we are able to follow the location of defect gap levels in SiGe alloys for different alloying compositions. The method is tested for several properties of the alloys, with special emphasis in the local bond-length relaxations. Our results indicate a predominant Pauling character for the alloys, with a topological rigidity parameter a** lying between 0.7 and 0.8. A comparative study between the electrical properties of the interstitial carbon (Ci) and carbon-oxygen (CiOi) centers in the alloys, shows that these complexes interact weakly with Ge atoms. The CiOi defect is predicted to produce a hole trap that varies as ΔE(0/+)=0.41-0. 76x eV, implying its disappearance for Ge fractions x greater than ∼0.5.