  Due to cost concerns, it is optimal to gain insight into the connectivity of
biological and other networks using as few experiments as possible. Data
selection for unique network connectivity identification has been an open
problem since the introduction of algebraic methods for reverse engineering for
almost two decades. In this manuscript we determine what data sets uniquely
identify the unsigned wiring diagram corresponding to a system that is discrete
in time and space. Furthermore, we answer the question of uniqueness for signed
wiring diagrams for Boolean networks. Computationally, unsigned and signed
wiring diagrams have been studied separately, and in this manuscript we also
show that there exists an ideal capable of encoding both unsigned and signed
information. This provides a unified approach to studying reverse engineering
that also gives significant computational benefits.
