We study networks of self avoiding polymer chains of arbitrary but fixed topology and calculate critical exponents governing their scaling properties (star exponents). Calculations are performed in the frames of the fixed-dimension field theoretical approach. Renormalization group functions in the Callan-Symanzik scheme are obtained in three-loop approximation and are analysed directly in three dimensions. Perturbation theory expansions are resummed with the use of Pad\'e-Borel transformation. The results obtained are in a good agreement with Monte-Carlo and $\varepsilon$-expansion data.