WANG Chengjunwangchj04@gmail.com     2010.12.24
 The characteristics of Diffusion Diffusion is a special case of brokerage Time dimension Relationships as channel Th...
 Empirical data Innovations of new mathematics method in  1950, Allegheny County, Pennsylvania, U.S.A. School superinte...
   Read data   ------------------------------------------------------------------------------   Reading Network --- E:l...
MODMATH.NET                               MODMATH_ADOPTION.CLU   *Vertices 38                              *Vertices 38 ...
 Two-step flow model First phase: Mass media inform and influence  opinion leaders Second phase: opinion leaders influe...
   Personal characteristics   The type of innovations   Perceived risk of innovations   Network structure:   In a den...
   Dimension: 38   The lowest value: 1                                                                  Diffusion curve...
 Create a random network Net> Random Network> Vertices Output  Degree Out-degree 1 or 2 No multiple lines Pick a vert...
diffusion curve of random network                  40                                                                     ...
 Everyone is unequally susceptible to contagion Two approaches to evaluate innovativeness: Adoption categories Classif...
We first choose time 2 (1959), and calculate the exposure at the time 2.And then, calculate time 3, time4, time 5, time6
   Net> Transform> Arcs->Edges>ALL
   Partition> Binarize (fill in 1-2)   Adoption time 1 & 2 are assigned a score of    1, and others are assigned a score...
FILL IN 1-2
   Operations> Vector> Summing up neighbors
   Because we defined exposure as the    percentage of neighbors who have adopted.   Vectors> First vector   Net> Parti...
Macro> PlayOptions> Read/Write>0/0Making new macro:Macro> Record----- Macro> Record
Results supplied by the author
   Read Project   Operations> Transform> Direction> Lower-    Higher
   Threshold=in-degree/ all-degree   in-degree is the in-degree of network which is directed    and having no multiple l...
   Record macro   Read project   Draw partition   Net> partitions > Degree> ALL   Vectors> Second vectors   Read pro...
   NETBEGIN 1   CLUBEGIN 1   PERBEGIN 1   CLSBEGIN 1   HIEBEGIN 1   VECBEGIN 1   Msg Reading Pajek Project File ---...
Net> Transform> Arcs->Edges> AllNet> Vector> Centrality> BetweennessInfo > Vector
   A threshold lag is a period in which an actor    does not adopt although he or she is exposed    at the level at which...
Tools> SPSS> Locate SPSSTools> SPSS> Send to SPSS
Diffusion curve             40                                                        38Adoption number                   ...
Calculate Thresholds of Diffusion with Pajek
Calculate Thresholds of Diffusion with Pajek
Calculate Thresholds of Diffusion with Pajek
Calculate Thresholds of Diffusion with Pajek
Calculate Thresholds of Diffusion with Pajek
Calculate Thresholds of Diffusion with Pajek
Calculate Thresholds of Diffusion with Pajek
Calculate Thresholds of Diffusion with Pajek
Calculate Thresholds of Diffusion with Pajek
Calculate Thresholds of Diffusion with Pajek
Calculate Thresholds of Diffusion with Pajek
Calculate Thresholds of Diffusion with Pajek
Calculate Thresholds of Diffusion with Pajek
Calculate Thresholds of Diffusion with Pajek
Calculate Thresholds of Diffusion with Pajek
Calculate Thresholds of Diffusion with Pajek
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Calculate Thresholds of Diffusion with Pajek

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Calculate Thresholds of Diffusion with Pajek

  1. 1. WANG Chengjunwangchj04@gmail.com 2010.12.24
  2. 2.  The characteristics of Diffusion Diffusion is a special case of brokerage Time dimension Relationships as channel The combination of structural positions & adoption time
  3. 3.  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
  4. 4.  Read data ------------------------------------------------------------------------------ Reading Network --- E:lingfei wupajek125ESNAdataChapter8ModMath.net ------------------------------------------------------------------------------ Reading Partition --- E:lingfei wupajek125ESNAdataChapter8ModMath_adoption.clu ------------------------------------------------------------------------------
  5. 5. MODMATH.NET MODMATH_ADOPTION.CLU *Vertices 38  *Vertices 38  4  1  4 1 "v1" 0.0500 0.5346 0.5000  4 2 "v2" 0.2300 0.7423 0.5000  2  4 3 "v3" 0.2300 0.6038 0.5000  2  4 ...........  2  4 *Arcs  2  4 *Edges  3  4 2 32 1  3  4  3  4 2 23 1  5 2 3 1  3  5 ……………….  3  5  3  5  3  5  3  5  3  5  3  5  6  4  6  4  6
  6. 6.  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
  7. 7.  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.
  8. 8.  Dimension: 38 The lowest value: 1 Diffusion curve The highest value: 6 The highest clusters values: 40 new 38 Rank Vertex Cluster Id 35 35 -------------------------------- cummulative Adoption number 1 38 6 v38 30 Frequency distribution of cluster 27 numbers: 25 Cluster Freq Freq% CumFreq 20 CumFreq% Representative ----------------------------------------------- 15 15 ---------------- 12 1 1 2.6316 1 2.6316 v1 10 10 2 4 10.5263 5 13.1579 v2 5 8 3 10 26.3158 15 39.4737 v6 5 1 4 4 12 31.5789 27 71.0526 3 v16 0 1 5 8 21.0526 35 92.1053 v28 6 3 7.8947 38 100.0000 v36 ----------------------------------------------- 1 2 3 4 5 6 ---------------- Sum 38 100.0000 Year
  9. 9.  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
  10. 10. 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
  11. 11.  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.
  12. 12. We first choose time 2 (1959), and calculate the exposure at the time 2.And then, calculate time 3, time4, time 5, time6
  13. 13.  Net> Transform> Arcs->Edges>ALL
  14. 14.  Partition> Binarize (fill in 1-2) Adoption time 1 & 2 are assigned a score of 1, and others are assigned a score of 0.
  15. 15. FILL IN 1-2
  16. 16.  Operations> Vector> Summing up neighbors
  17. 17.  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 !!!!!!!
  18. 18. Macro> PlayOptions> Read/Write>0/0Making new macro:Macro> Record----- Macro> Record
  19. 19. Results supplied by the author
  20. 20.  Read Project Operations> Transform> Direction> Lower- Higher
  21. 21.  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”.
  22. 22.  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
  23. 23.  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 [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 [0] (38) V 3 DIVV 2 1 (38)
  24. 24. Net> Transform> Arcs->Edges> AllNet> Vector> Centrality> BetweennessInfo > Vector
  25. 25.  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).
  26. 26. Tools> SPSS> Locate SPSSTools> SPSS> Send to SPSS
  27. 27. 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

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