Before revision:  Robust motifs are graphs associated to threshold-linear networks (TLNs) for which the structure of fixed points  is independent of the choice of connectivity matrix W . In this work we describe infinite families of robust motifs, and use them to completely characterize all robust motifs for networks of size n \leq 5. These graph structures tightly constrain the dynamics of the associated TLNs, making them ideal candidates for constructing network architectures whose dynamics are robust despite allowing great flexibility in the choice of W .
After revision:  Robust motifs are graphs associated to threshold-linear networks (TLNs) for which the structure of fixed points is independent of the choice of connectivity matrix W , and whose dynamics are thus greatly constrained. This makes them ideal building blocks for constructing larger networks whose behaviors are robust to changes in connection strengths. In contrast, flexible motifs correspond to networks with multiple dynamic regimes. In this work, we give a purely graphical characterization of both flexible and robust motifs of any size. We find that all but a few robust motifs fall into two infinite families of graphs with simple feedforward architectures .