Several users of our AS relationship inference data (http://www.caida.org/data/active/as-relationships/), released with cs/0604017, asked us why it contained AS relationship cycles, e.g., cases where AS A is a provider of AS B, B is a provider of C, and C is a provider of A, or other cycle types. Having been answering these questions in private communications, we have eventually decided to write down our answers here for future reference.
Cite
@article{arxiv.0807.0887,
title = {On Cycles in AS Relationships},
author = {Xenofontas Dimitropoulos and M. Angeles Serrano and Dmitri Krioukov},
journal= {arXiv preprint arXiv:0807.0887},
year = {2008}
}