Figure 2

Using the same networks as Fig. 1 (shown in the inset of subfigure (A)), we compare the same pairs using the BiDir distance, shown in (A). We notice that distance between the pair A–C is small, as demonstrated by a BiDir value very close to the origin and identity line. Similarly, if we project the communities of A onto network E, we obtain a very good fit and a near zero distance (as shown by the point on the x axis). This is a consequence of the fact that the communities of E are a refinement of the ones in A. This does not hold true in the other direction, i.e., if we project the communities of E onto A, as shown by a non-zero distance of the point to the y axis. On the right, in (B) and (C), we can see how rankings derived from other metrics, such as NMI and spectral distance, do not fully capture these features. For NMI, the A–E pair is similar, but not so for the spectral distance