  We show that the average size of self-avoiding polygons (SAP) with a fixed
knot is much larger than that of no topological constraint if the excluded
volume is small and the number of segments is large. We call it topological
swelling. We argue an "enhancement" of the scaling exponent for random polygons
with a fixed knot. We study them systematically through SAP consisting of hard
cylindrical segments with various different values of the radius of segments.
Here we mean by the average size the mean-square radius of gyration.
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 by such a number of segments that
topological entropic repulsions are balanced with the knot complexity in the
average size. The additivity suggests the local knot picture.
