Figure 3

We illustrate our framework using three different families of SBMs. In family A all five networks contain the same communities, but the strength of in-group ties is sequentially decreasing. In subfigure (D) we see that the distances are zero whenever the original communities are detected, and increase with the weakening of the community structure. In family B each successive SBM is a refinement of the previous one, with blocks splitting along the way. So while B1 has two large communities, B3 has 4 communities, two for each of B1’s communities. Notice that in subfigure (E), the community structure of B1 describes well the structure of B2–B5, but that doesn’t hold in the other direction. In the last family of SBMs C1 has three communities while C2 and C3 have four identical communities. But for C2, two of these communities can also be merged into one larger community. In subfigure (F) we can see that, while C2 and C3 have an identical optimal community structure, our method picks up that C1 is closer to C3 than to C2 because C3 can also be partitioned into 3 communities