Difference between revisions of "Snapshot"

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

Latest revision as of 16:53, 4 April 2011

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:

Snapshot.jpg

As with ordinal time, it is now useful to define as the ratio of two quantities, , where is the number of triples (u;C; k) for which u was k-exposed to C at time t1, and 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.