This paper considers the hammock networks introduced by Moore and Shannon in 1956. We mention reliability polynomials (including some of their properties) and go briefly over the state-of-the-art: theoretical, algorithmic and design oriented. These are advocating for using (small) hammock networks as a perfect fit for array-based designs of nano-devices (like, e.g., FinFETs, SegFETs, VFETs, VeSFETs, and various nanotubes transistors). Because array-based designs are expected to thrive, we have decided to take a very close look at small hammock networks. That is why we have calculated exactly the reliability polynomials of small hammock networks. As far as we know, the non-trivial reliability polynomials are reported here for the first time ever. The coefficients of the reliability polynomials have been determined using our own program, and knowing all of them exactly is intended for practicality (as hammock networks might play a central role in array-based designs). The paper ends with conclusions and future directions of research.