We show that the mean-square radius of gyration for random polygons (RP) with fixed knot and that of self-avoiding polygons (SAP) with fixed knot are much larger than those of no topological constraint, respectively, if the number of segments $N$ is large and for SAP the excluded volume is small. We call it topological swelling. In particular, we argue that the effective scaling exponent of RP with fixed knot is enhanced and approaches the scaling exponent of self-avoiding walks if the number of segments $N$ goes to infinity. We study them systematically through SAP consisting of impenetrable cylindrical segments for various different values of the radius of segments. Furthermore, we show numerically that the equilibrium length of a composite knot is given by the sum of those of all constituent prime knots. Here we define the equilibrium length of a knot in RP or SAP by such a number of segments that the topological entropic repulsions are balanced with the complexity of the knot in the mean-square gyration radius for RP or SAP with the fixed knot. The additivity suggests the local knot picture in knotted RP or SAP. The present talk is based on the research in collaboration with Erica Uehara.