Snapshot

Snapshot: Consider two snapshots of the network at different points in time. For each k, consider the set of all individuals who are k-exposed in the first snapshot. Let ps(k) be the fraction of individuals in this set who have become adopters by the time of the second snapshot.

Figure 2 shows the shape of influence curves for the snapshot definitions using the Wikipedia data:

As with ordinal time, it is now useful to define $p_{s}\left(k\right)$ as the ratio of two quantities, $p_{s}\left(k\right)=n_{s}\left(k\right)/d_{s}\left(k\right)$, where $d_{s}\left(k\right)$ is the number of triples (u;C; k) for which u was k-exposed to C at time t1, and $n_{s}\left(k\right)$ is the number of triples (u,C,k) for which u was k-exposed to C at time t1, and then joined C between t1 and t2.