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. 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
9. 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
10.
11. 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.
13. 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
14. diffusion curve of random network
40
38
35 35
Adoption 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
15. 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.
16. We first choose time 2 (1959), and calculate the exposure at the time 2.
And then, calculate time 3, time4, time 5, time6
21. 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 !!!!!!!
31. 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”.
32. 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
33. 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)
36. 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).