Fig. 17
From: Path homologies of motifs and temporal network representations
(L) Betti numbers of the temporal digraph representation of the (L) MathOverflow and (R) Facebook DCNs. In the former case, we used a window of eight hours (this is different than in other representations, and was done for the sake of scaling), whereas in the latter case we used a window of 24 hours, as in other representations. Note that in the latter case \(\beta _0\) is also the same as for the MLP representation. For some later times with both networks, \(\beta _2\) could not be computed due to memory constraints, but was always zero when computed, including near the beginning of the MathOverflow DCN. Recomputing the Betti numbers for \(p < 2\) required just a few minutes