Mechanisms of redundancy. (A) All genes function as parts of pathways (e.g. A-H, shown as yellow spheres). Some genes (e.g., a-m, shown as purple squares) affect one another and form a gene sub-network (nodes are genes, and edges, shown as blue lines, describe correlations,). Theoretically, if we assume only two pathways (A and B), this gene sub-network can be simplified to a single edge/crosstalk between the two pathways (gray lines). The perturbation of a single gene may not significantly affect the expression of this pathway crosstalk. Thus, the redundant genes in each pathway and their connectivity may act as a resistance mechanism. Moreover, each instance of crosstalk may be regulated by another pathway and form a simple network structure, such as triangle/3-node circle. If the network is well connected, a single crosstalk may be included in many 3-node circles (i.e., redundant paths per crosstalk). An indirect approach to perturb a crosstalk would be through its shortest paths. Having many alternative paths may lead to formation of a robust structure. Lastly, those alternative 3-node circles may be grouped together into categories (e.g., 1–4 in magenta diamonds) based on their biological system (e.g., pathways G and H share the same category number 4). Thus, instead of having six 3-node circles, we have two main category circles: – and ,,. These three mechanisms of redundancy reveal the impact of network structures on the level of resistance. (B) Our method of determining the pathway co-expression network is described here in steps as a flow chart (see Methods section for more details).