  It is known that the writhe calculated from any reduced alternating link
diagram of the same (alternating) link has the same value. That is, it is a
link invariant if we restrict ourselves to reduced alternating link diagrams.
This is due to the fact that reduced alternating link diagrams of the same link
are obtainable from each other via flypes and flypes do not change writhe. In
this paper, we introduce several quantities that are derived from Seifert
graphs of reduced alternating link diagrams. We prove that they are
"writhe-like" invariants in the sense that they are also link invariants among
reduced alternating link diagrams. The determination of these invariants are
elementary and non-recursive so they are easy to calculate. We demonstrate that
many different alternating links can be easily distinguished by these new
invariants, even for large, complicated knots for which other invariants such
as the Jones polynomial are hard to compute. As an application, we also derive
an if and only if condition for a strongly invertible rational link.
