Question 1
Below are social network data collected from members of a book club at a university. The students were asked to rate ‘how much they interacted online’ with the other students over the last two weeks on a five-point Likert scale with ‘1’ being ‘very little’ and ‘5’ being ‘a great deal’.
Mark Gene 5
Mark Silvia 4
Mark Sarah 4
Mark Tim 2
Gene Mark 2
Gene Silvia 2
Gene Sarah 3
Gene Tim 4
Silvia Mark 2
Silvia Gene 2
Silvia Sarah 4
Silvia Tim 4
Sarah Mark 2
Sarah Gene 1
Sarah Silvia 2
Sarah Tim 4
Tim Mark 1
Tim Gene 3
Tim Silvia 2
Tim Sarah 4
a. Enter the data in a spreadsheet using the adjacency matrix format and save the result as a CSV file.
"ID","Gene","Mark","Sarah","Silvia","Tim"
"Gene",0,2,3,2,4
"Mark",5,0,4,4,2
"Sarah",1,2,0,2,4
"Silvia",2,2,4,0,4
"Tim",3,1,4,2,0
b. Import the data into an xUCINET project.
BookClub<-xCreateProject(GeneralDescription="Members of a university book club.",
NetworkName="Interaction",
NETFILE="C:/Users/Steve Borgatti/Documents/ucinet data/asnrp51.csv",
FileType="csv",
InFormatType="AdjMat",
NetworkDescription="Amount of online interaction 1= very little to 5 = a great deal",
Mode=c("People"),
Directed=TRUE,
Loops=FALSE,
Values="Ordinal",
Class="matrix",
References="No references")
BookClub$Interaction
Gene Mark Sarah Silvia Tim
Gene 0 2 3 2 4
Mark 5 0 4 4 2
Sarah 1 2 0 2 4
Silvia 2 2 4 0 4
Tim 3 1 4 2 0
It is somewhat surprising that the matrix is so asymmetric.
c. Symmetrize the data using the minimum.
intsym <- xSymmetrize(BookClub$Interaction)
d. Dichotomize the symmetrized data using greater than 3.
intsymdichgt3 <- xDichotomize(intsym,Value=3)
intsymdichgt3
Gene Mark Sarah Silvia Tim
Gene 0 0 0 0 0
Mark 0 0 0 0 0
Sarah 0 0 0 0 1
Silvia 0 0 0 0 0
Tim 0 0 1 0 0
e. Save the data (as a .RData file), and also export it as a CSV file.
save(intsymdichgt3, file = "intsymdichgt3.RData")
write.csv(intsymdichgt3, file = "intsymdichgt3.csv" )
"","Gene","Mark","Sarah","Silvia","Tim"
"Gene",0,0,0,0,0
"Mark",0,0,0,0,0
"Sarah",0,0,0,0,1
"Silvia",0,0,0,0,0
"Tim",0,0,1,0,0
f. What would have happened if we had first dichotomized the data using the ‘greater than 3’ rule, and subsequently symmetrized the data using the minimum?
# the result is the same
intdichgt3 <- xDichotomize(BookClub$Interaction, Value = 3)
intdichgt3sym <- xSymmetrize(intdichgt3)
intdichgt3sym
all(intsymdichgt3 == intdichgt3sym)
[1] TRUE
g. Save the dichotomized symmetrize matrix back into the BookClub project.
online <- intdichgt3sym
BookClub <- xAddToProject(BookClub,
NETFILE1=online,
NetworkName="Online interaction",
FileType = "Robject")
Problem 2
Demographic and attribute data were also collected (see below). Data include age, gender and attitude towards premarital sex on a Likert scale from 1 to 5 (with ‘1’ being ‘completely against’ and ‘5’ being ‘completely in favor’).
Age Gender (1=male, 2=female) Attitude towards premarital sex (1= against, 5 = in favor)
Mark 18 1 4
Gene 25 1 2
Silvia 19 2 2
Sarah 21 2 5
Tim 22 1 1
a. Enter the data in a matrix format in a csv file
# put rows in same order as the network matrix in problem 1
"ID","Age","Attitude","Female"
"Gene",25,2,0
"Mark",18,4,0
"Sarah",21,5,1
"Silvia",19,2,1
"Tim",22,1,0
b. Add the data to the xUCINET project dataset that contains the network from Problem 1
BookClub <- xAddAttributesToProject(ProjectName = BookClub,
ATTFILE1="C:/Users/steve borgatti/Documents/asnr/bookclubattr.csv",
FileType="csv",
Mode=c("People"),
AttributesDescription=c("Age in years","Female (0=Male, 1=Female)","Attitude toward premarital sex (1= against, 5 = in favor)"))
BookClub$Attributes
NodeName Age Attitude Female
1 Gene 25 2 0
2 Mark 18 4 0
3 Sarah 21 5 1
4 Silvia 19 2 1
5 Tim 22 1 0
.
c. Convert the Attitude variable into a node-by-node matrix using absolute difference. What do the values represent?
attabsdiff <- xAttributeToNetwork(BookClub$Attributes$Attitude, Type="AbsDiff")
> attabsdiff
[,1] [,2] [,3] [,4] [,5]
[1,] 0 2 3 0 1
[2,] 2 0 1 2 3
[3,] 3 1 0 3 4
[4,] 0 2 3 0 1
[5,] 1 3 4 1 0
The matrix shows how different in attitude towards pre-marital sex each pair of persons is. Nodes 3 and 5 (Sarah and Tim) are the most different in attitude (bad news for Sarah).
d. Convert the Gender variable into a node-by-node matrix using the difference. What does this result in?
attdiff <- xAttributeToNetwork(BookClub$Attributes$Attitude, Type="Diffij")
> attdiff
[,1] [,2] [,3] [,4] [,5]
[1,] 0 -2 -3 0 1
[2,] 2 0 -1 2 3
[3,] 3 1 0 3 4
[4,] 0 -2 -3 0 1
[5,] -1 -3 -4 -1 0
The result gives the row node's attitude minus the column node's attitude. Node 1's attitude minus Node 2's equals -2: Node 1 is less in favor of premarital sex than node 2.
Problem 3
In addition to the one-mode social network data above, two-mode data were also collected on which university events each had attended over the last six months. Here are the data:
• Mark went to Hawking’s Lecture
• Gene went to Hawking’s Lecture and Spring Concert
• Silvia went to Hawking’s Lecture, Halloween Event, and Fall Dance
• Sarah went to Hawking’s Lecture, Halloween Event, Spring Concert, and Fall Dance
• Tim went to Halloween Event, Spring Concert, and Fall Dance
a. Format the data as a spreadsheet file using an adjacency matrix format, and save as a CSV file. [Note: the original question asked for a nodelist format, but this has not been implemented yet.]
"ID","Fall_Dance","Halloween_Event","Hawking_Lecture","Spring_Concert"
"Gene",0,0,1,1
"Mark",0,0,1,0
"Sarah",1,1,1,1
"Silvia",1,1,1,0
"Tim",1,1,0,1
b. Add the network to the project (from Problems 1 and 2) as a matrix object, and check the output when calling the resulting object.
BookClub<-xAddToProject(ProjectName=BookClub,
NetworkName="Attendance",
NETFILE1="C:/Users/steve borgatti/Documents/asnr/bookclubattendance.csv",
FileType="csv",
InFormatType="AdjMat",
NetworkDescription="Attendance at university events",
Mode=c("People","Events"),
Directed=FALSE,
Values="Binary",
Class="matrix")
BookClub$Attendance
Fall_Dance Halloween_Event Hawking_Lecture Spring_Concert
Gene 0 0 1 1
Mark 0 0 1 0
Sarah 1 1 1 1
Silvia 1 1 1 0
Tim 1 1 0 1
Problem 4
Finally, the students were asked who talks to whom about school-related matters.
• Mark reports he talks to Gene, Silvia, and Sarah
• Gene reports he talks to Tim
• Silvia reports she talks to Tim and Sarah
• Sarah reports she talks to Tim
• Tim reports he talks to Sarah
a. Enter the data using the edgelist format and save as a CSV file. Import into R
Gene,Mark
Gene,Tim
Mark,Sarah
Mark,Silvia
Sarah,Silvia
Sarah,Tim
Silvia,Tim
fn = "c:/Users/steve borgatti/Documents/asnr/bookclubtalkstoel.csv"
dt <- read.csv(fn)
g <- igraph::graph.data.frame(dt, directed=TRUE)
talksto <- igraph::as_adj(g,sparse=FALSE)
talksto <- talksto[order(rownames(talksto)),order(colnames(talksto))]
talksto
Gene Mark Sarah Silvia Tim
Gene 0 0 0 0 0
Mark 1 0 1 1 0
Sarah 0 0 0 0 1
Silvia 0 0 1 0 1
Tim 0 0 1 0 0
b. Symmetrize the network using the ‘OR’ approach.
talkstosym <- xSymmetrize(talksto,Type="Max")
talkstosym
Gene Mark Sarah Silvia Tim
Gene 0 1 0 0 0
Mark 1 0 1 1 0
Sarah 0 1 0 1 1
Silvia 0 1 1 0 1
Tim 0 0 1 1 0
Problem 5
Imagine you would want to combine the dichotomized online interaction network (Problem 1) and the face-to-face talking network (Problem 4) into one matrix.
a. How would you go about making sure you are able to distinguish between ties where (a) members only talk face-to-face, but do not interact online, (b) members who only interact online, but not face-to-face, (c) where members do both, and (d) where members do neither? Import both datasets into R and use R to solve this.
f2f = talkstosym*2 #created in the last problem
interactswith = online + f2f #onine created in probem 1
interactswith
Gene Mark Sarah Silvia Tim
Gene 0 2 0 0 0
Mark 2 0 2 2 0
Sarah 0 2 0 2 3
Silvia 0 2 2 0 2
Tim 0 0 3 2 0
In this matrix, a 1 would mean online only, a 2 means f2f only, and a 3 means both online and face to face.
b. Given the type of data, could you consider a different approach of combining both data? Reflect on your answer.