Figure 4: We only show the central part, see Figure 2, of the network of 379 network scientists since all loops occur here (a). We find the first relatively small loop between four scientists for appearing for threshold weight 1. As we decrease the threshold weight, more loops appear. Notice how we have shaded two triangles for ; this is to indicate that there is no loop there; there are three new blue loops added at this stage. We notice that for smaller threshold values we find larger loops. In (b) we show the barcode for the first Betti numbers of this filtration. In (c) we enlist the length of the loops that appear at each filtration value.