Consider the following terms.
• conjoined, “Joined together, as with conjoined twins, or in matrimony”
• bonded, using senses of bond such as “A physical connection which binds, a band; often plural”, “An emotional link, connection or union”, and “Any constraining or cementing force or material”
• friendly, reflecting that the two strings are quite alike
• twined, using the “to become mutually involved” sense of twine
• woven, using the “To unite by close connection or intermixture” sense of weave
• mutual, adj., “Possessed in common”; you would use it as a noun, after properly defining it: “We call strings α and β mutual if...”

Consider the following terms.
• conjoined, “Joined together, as with conjoined twins, or in matrimony”
• bonded, using senses of bond such as “A physical connection which binds, a band; often plural”, “An emotional link, connection or union”, and “Any constraining or cementing force or material”
• friendly, reflecting that the two strings are quite alike
• twined, using the “to become mutually involved” sense of twine
• woven, using the “To unite by close connection or intermixture” sense of weave
• mutual, adj., “Possessed in common”; you would use it as a noun, after properly defining it: “We call strings α and β mutual if...” • neighbors, in the sense “situated adjacently or nearby”
• proximate, “Close or closest; adjacent”
• propinquinous (or even pinquinous), as formations based on propinquity, “Nearness or proximity; Affiliation or similarity”; or the Latin form propinquus, which has the following senses: “(of space) near, neighboring; (of time) near, at hand, not far off; (of appearance) resembling, similar, like, alike; (of a relationship) kindred, related”