What is the wire running from the CG to the tail?
Sounds like an HF antenna. It absolutely isn't structural, as neither of those aircraft needs guy-wires for structural stability. (You'd also expect to see it on every example, not just some, if it were required that way.)

This article provides a lengthy discussion of HF antennae, for those interested in going deeper into the subject.

This thread has a related discussion of why not all HF antennae are of the long-wire type. Essentially, newer designs often replace the long wires.