Ordinal-time
Ordinal-time: Consider a complete time sequence of an evolving social network that includes each time a new network link is formed and each time an individual adopts a new behavior. For each k, consider the set of all individuals who were ever k-exposed at any time, and define po(k) to be the fraction of this set that became adopters before acquiring a (k + 1)st neighbor who is an adopter.
Figure 1 shows the shape of influence curves for the ordinal-time definitions using the Wikipedia data:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle p_{o}\left ( k \right )} is the fraction of cases in which a node that is k-exposed to a community C proceeds to join C before acquiring a (k + 1)st neighbor in C. That is, we define Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle p_{o}\left ( k \right )} as the ratio of two quantities, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle p_{o}\left ( k \right )=n_{o}\left ( k \right )/d_{o}\left ( k \right )} , where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle d_{o}\left ( k \right )} is the number of triples (u;C; k) for which u was ever k-exposed to C, and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n_{o}\left ( k \right )} is the number of triples (u,C,k) for which u was k-exposed to C, and then joined C before acquiring a (k + 1)st neighbor in C.
