Networking Seifert surgeries on knots

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How do Seifert surgeries on hyperbolic knots arise from those on torus knots? We approach this question from a networking viewpoint. Our basic idea is finding relationships among such surgeries using ``inheritance" property of seiferters. A path in the network from one Seifert surgery to another explains how the former Seifert surgery is obtained from the latter after a sequence of twistings along seiferters and/or annuli cobounded by pairs of seiferters. We find explicit paths from various known Seifert surgeries to those on torus knots, the most basic and well-understood Seifert surgeries. Successive twists along a ``hyperbolic seiferter" or a ``hyperbolic annular pair" produce infinitely many Seifert surgeries on hyperbolic knots. We have given a list of Seifert surgeries on torus knots which have hyperbolic seiferters or hyperbolic annular pairs, and obtained results suggesting that such surgeries are restricted.