The characteristics of Diffusion Diffusion is a special case of brokerage Time dimension Relationships as channel The combination of structural positions & adoption time
Empirical data Innovations of new mathematics method in 1950, Allegheny County, Pennsylvania, U.S.A. School superintendents as gatekeepers Nomination method: ask the respondents to indicate their three best friends The social network is named modern math network
Two-step flow model First phase: Mass media inform and influence opinion leaders Second phase: opinion leaders influence potential adopters Diffusion of innovations Opinion leaders use social relations to influence their contacts Advice and friendship relations
Personal characteristics The type of innovations Perceived risk of innovations Network structure: In a dense network an innovation spreads more easily and faster than in a sparse network, In an unconnected network diffusion will be slower and less comprehensive than in a connected network, In a bi-component diffusion will be faster than in components with cut-points or bridges, The larger the neighborhood of a person within the network, the earlier s/he will adopt an innovation, A central position is likely to lead to early adoption, Diffusion from a central vertex is faster than from a vertex in the margins of the network.
Create a random network Net> Random Network> Vertices Output Degree Out-degree 1 or 2 No multiple lines Pick a vertex as the source of diffusion process Assume a vertex will adopt at the first time point after it has established direct contact with an adopter
diffusion curve of random network 40 38 35 35Adoption number 30 new 25 cummulative 25 20 15 15 10 10 4 10 5 1 6 3 3 0 1 1 2 3 4 5 6 year
Everyone is unequally susceptible to contagion Two approaches to evaluate innovativeness: Adoption categories Classify people by their adoption time: Innovators, early adopters, early majority, late adopters, laggards. It’s useful to identify the social and demographic characteristics Threshold categories: The threshold is his or her exposure at the time of adoption The exposure of a vertex in a network at a particular moment is the proportion of its neighbors who have adopted before that time Some people are easily persuaded (more susceptible) than others However, individual thresholds are computed after the fact, which is a hindsight and not informative. They should be validated by other indicators of innovativeness.
We first choose time 2 (1959), and calculate the exposure at the time 2.And then, calculate time 3, time4, time 5, time6
Because we defined exposure as the percentage of neighbors who have adopted. Vectors> First vector Net> Partitions> Degree There aren’t the Partition> Make vector (do not normalize) submenus of first Vectors> Second vector vector and second Vectors> Divide First by Second vector in Options> Read/Write>0/0 PAJEK125 !!!!!!!
Macro> PlayOptions> Read/Write>0/0Making new macro:Macro> Record----- Macro> Record
Threshold=in-degree/ all-degree in-degree is the in-degree of network which is directed and having no multiple lines and no lines within classes all-degree is the all-degree of network which is undirected and having n0 multiple lines Because the original network is undirected and having no multiple lines, so we can calculate all-degree directly. To obtain the in-degree, we should re-read original network and change it into directed one which has no lines within classes first, and then we can calculate in-degree directly. Using the submenu “divide first by second” in the menu of “Vectors”, we can get the threshold. Draw the vectors, and “mark vertices using” “vector values”.
Record macro Read project Draw partition Net> partitions > Degree> ALL Vectors> Second vectors Read project Operations> Transform> Direction Net> partitions > Degree> Input Vectors> First vectors Vectors> Divide First by Second Draw> Draw-vector Record macro
NETBEGIN 1 CLUBEGIN 1 PERBEGIN 1 CLSBEGIN 1 HIEBEGIN 1 VECBEGIN 1 Msg Reading Pajek Project File --- E:lingfei wupajek125ESNAdataChapter8ModMath.paj Msg Reading Network --- ModMath_directed.net Msg Reading Network --- ModMath.net Msg Reading Partition --- ModMath_adoption.clu N 9999 RDPAJ ? N 2 LAYERSNX 2 1 Msg Optimizing total length of lines ... Msg All degree centrality of 2. ModMath.net (38) C 2 DEGC 2  (38) N 3 ETOAINC 2 1 1 DEL (38) Msg Input degree centrality of 3. Directed Network [INC DEL] of N2 according to C1 (38) C 3 DEGC 3  (38) V 3 DIVV 2 1 (38)
A threshold lag is a period in which an actor does not adopt although he or she is exposed at the level at which he or she will adopt later. The critical mass of a diffusion process is the minimum number of adopters needed to sustain a diffusion process. V28 and V29 undergoes a threshold lag, respectively (we can tell that from the pic of thresholds).
Tools> SPSS> Locate SPSSTools> SPSS> Send to SPSS
Diffusion curve 40 38Adoption number new 35 30 27 20 15 10 10 12 5 8 1 4 3 0 1 1 2 3 4 5 6 Year