Classification of 3-node restricted excitatory-inhibitory networks

We classify connected 3-node restricted excitatory-inhibitory networks, extending our previous paper (Aguiar et al., 2024). We assume that there are two node-types and two arrow-types, excitatory and inhibitory; all excitatory arrows are identical and all inhibitory arrows are identical; and excitatory (resp. inhibitory) nodes can only output excitatory (resp. inhibitory) arrows. The classification is performed under the following two network perspectives: ODE-equivalence and minimality; and valence ≤2. The results of this and the previous work constitute a first step towards analyzing dynamics and bifurcations of excitatory-inhibitory networks and have potential applications to biological network models.