Skyscraper

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A Skyscraper is a same-digit two strong link chain. Its two strong links come from conjugate pairs in two rows or two columns. When drawn on the board, those two strong links are parallel.

For a given candidate digit, if you can find two conjugate-pair strong links in two rows or two columns, and choose one node from each strong link so that those two chosen nodes lie in the same column or row and therefore form a weak link, then the pattern is a Skyscraper. The two unchosen nodes are the endpoints of the chain. Any candidate that forms weak links with both endpoints can be eliminated.

For example, look at digit $4$ in the board below. In columns $C2$ and $C9$, there are two parallel conjugate pairs, because $4$ appears exactly twice in each of those columns. At the same time, $R7C2$ and $R7C9$ lie in the same row, so they form a weak link. This gives a two-strong-link chain with endpoints $R1C2$ and $R2C9$. By the logic of alternating inference chains, those two endpoints also act as a strong link, so one of them must be true. Candidate $4$ in each of $R1C8$ and $R2C3$ forms weak links with both endpoints, so these candidates can be eliminated.

This is a very clean example of a Skyscraper. If you think of the horizontal weak link as the horizon, the two vertical strong links look like two skyscrapers. But the technique only requires the two strong links to be parallel. They do not have to stand upright.

For example, in the next board, digit $1$ forms two parallel strong links: one between $R3C1$ and $R3C8$, and the other between $R5C2$ and $R5C8$. The cells $R3C8$ and $R5C8$ lie in the same column and form a weak link, so the endpoints are $R3C1$ and $R5C2$. That lets us eliminate candidate $1$ from $R1C2$, $R2C2$, $R4C1$, and $R6C1$.

Note that a Skyscraper can often eliminate more than one candidate. Because the two strong links are parallel and lie in rows or columns, the boxes containing the two endpoints may each contain candidates that form weak links with both endpoints. So when you find the basic shape, inspect both endpoint boxes carefully.

Here are two more Skyscraper examples in other orientations.