# Simulating Ordinal Time from Snapshots

Roughly, the simulation works by hypothesizing the number of neighbors each node had at the moment it joined a community; choosing this number from among the possible values consistent with the snapshot observations. The authors exploit both the B(t1) and the J(t1,t2) sets. Recall the set B(t1) consists of triples (u,C,k1), where u joined C before t1, and u had k1 neighbors in C at t1. We choose an integer j uniformly at random in [0,k1] and assume that u had j neighbors in C at the time it joined C. Similarly, the set J(t1,t2) consists of tuples (u,C,k1,k2) where u joined C between t1 and t2, u had k1 neighbors in C at t1, and u had k2 neighbors in C at t2. Here we construct the approximation to ordinal-time by choosing an integer j uniformly at random from [k1,k2] and again assuming that that u had j neighbors in C at the time it joined C. Finally, we do not assume that u joins C for any tuple ${\displaystyle \left(u,C,k\right)\in N\left(t_{2}\right)}$.