Is there an asymmetric scheme where keys form a graph and a message can only be decrypted across a certain degree of separation?
This looks like a new research to be done. I believe this is doable starting from graph characteristic polynomial as introduced at iacr 2008/363 and CECC 2009 (shameless). "Trusted" relationship would mean knowing secrets associated with neighbor nodes. Having secrets of trusted network of neighbors, sender would produce characteristic polynomial such that any trusted node can divide, that is, produce zero remainder polynomial. There might be a variant of ElGamal encryption designed from probabilistic test (Schwartz-Zippel) for zero remainder condition, which would likely complete this design. Considering (verifying) characteristic polynomials over a ring modulo random linear polynomial (no such ring at 363 preprint yet) might be a practical solution. Welcome.