What type of glue or adhesive will bond monofilament fishing line?

By bond, I mean form a real chemical bond from one strand of fishing
line to another, and not simply form a hard shell around the strands
where they can still be pulled through after the adhesive cures.

I understand that most fishing line is basically nylon, and if so I
guess I'm looking for an adhesive specifically for nylon (yes?). I'm
trying to bond short pieces of fishing line across (or perpendicular
to) a longer length of line. So the glue would be applied at the node
where they cross.

Heating the strands to bond them together doesn't seem to work in a
predicatable way because the strands are too small (we're talking
about 10 to 15 lb fishing line).

Any ideas?