Fig. 3.

Illustration of violating (a) and redundant (b) edges (in gray) in a pathway with four genes. Edge $y_1\to v_1$ is violating because there is evidence that v₁ is placed upstream of y₁ ($v_1\to w_1$ and $w_1\to y_1$) but also that y₁ is upstream of v₁ ($y_1\to v_1$). Edge $u_2\to w_2$ is redundant because there is evidence of an intermediate gene $v_2.$ Similarly, edge $u_2\to y_2$ is redundant because of two intervening genes, v₂ and w₂