If A → B and C → process (A → B), where A → B is not a biochemical reaction such as an enzyme catalyzed reaction or protein–protein/small molecule interaction, we assume that C is acting on an intermediary node (IN) of the A–B pathway. This IN could be an intermediate protein complex, protein–small molecule complex, or multiple complexes (see Figure 1, panel 1). For example, ABA → closure, and NO synthase (NOS) → process (ABA → closure); therefore, ABA → IN → closure, NOS → IN. If A → B is a direct process such as a biochemical reaction or a protein–protein interaction, we assume that C → process (A → B) corresponds to C → A → B.

A → B and C → process (A → B) can be transformed to A → C → B if A → C is also documented. This means that the simplest explanation is to identify the putative intermediary node with C. For example, ABA → NOS, and NOS → process (ABA → NO) are experimentally verified and NOS is an enzyme producing NO, therefore, we infer ABA → NOS → NO (see Figure 1, panel 2).

A rule similar to rule 1 applies to inhibitory interactions (denoted by —|); however, in the case of A —| B, and C —| process (A —| B), the logically correct representation is: A → IN —| B, C —| IN (see Figure 1, panel 3).

The above rules constitute a heuristic algorithm for first expanding the network wherever the experimental relationships are known to be indirect, and second, minimizing the uncertainty of the network by filtering synonymous relationships. Mathematically, this algorithm is related to the problem of finding the minimum transitive reduction of a graph (i.e., for finding the sparsest subgraph with the same reachability relationships as the original) [14]; however, it differs from previously used algorithms by the fact that the edges can have one of two signs (activating and inhibitory), and edges corresponding to direct interactions are maintained.