  How do Seifert surgeries on hyperbolic knots arise from those on torus knots?
We approach this question from a networking viewpoint. The Seifert Surgery
Network is a 1-dimensional complex whose vertices correspond to Seifert
surgeries; two vertices are connected by an edge if one Seifert surgery is
obtained from the other by a single twist along a trivial knot called a
seiferter or along an annulus cobounded by seiferters. Successive twists along
a "hyperbolic seiferter" or a "hyperbolic annular pair" produce infinitely many
Seifert surgeries on hyperbolic knots. In this paper, we investigate Seifert
surgeries on torus knots which have hyperbolic seiferters or hyperbolic annular
pairs, and obtain results suggesting that such surgeries are restricted.
