Two mode Network
PAD 637, Lab 8
Spring 2013
Yoonie Lee
Lab exercises
• Two- mode
▫ Davis
• QAP correlation
• Multiple regression QAP
Types of network data
• One-mode network
(M × M )
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• Two-mode network
(M × N )
Two mode network data
• Check “davis.##h” in UCINET
▫ These data were collected by Davis et al. in the
1930s. They represent observed attendance at 14
social events by 18 Southern women.
▫ The result is a person-by-event matrix (18-by-14)
• Two mode networks are also called as
“affiliation" data
▫ because they describe which actors are affiliated
(present, or members of) which macro structures.
Two mode network data
• Basic idea of two-mode in davis data:
▫ By examining patterns of which women are present (or
absent) at which events,
 it is possible to infer an underlying pattern of social ties,
factions, and groupings among the women.
▫ At the same time, by examining which women were
present at the 14 events,
 it is possible to infer underlying patterns in the similarity
of the events.
▫ Let’s do a visualization with two mode data!
 Go to Netdraw with davis data
Ron Breiger (1974) “The duality of persons and
groups” calls for attention to the dual focus of
social network analysis on
(1) how individuals, by their agency, create social
structures (e.g., individual choice 
meaning of events)
(2) while, at the same time, how social structures
develop an institutionalized reality that
constrains and shapes the behavior of the
individuals embedded in them. (e.g., events
 choice of individuals)
Two mode network data
• With “davis.##h” in UCINET
▫ Convert two mode to one mode
▫ In UCINET> Data> Affiliations (2-mode to 1mode)
 Rows
 Columns
Who is most active actor?
Which event is the biggest one?
Let’s do some centrality analysis with
this converted matrix
• Let’s do the Freeman’s degree centrality measure
with converted women-by-women data
• What does this mean?
• What does 57 mean here?
• Think about converted matrix!
Theresa had 57 connections
through attending events.
Let’s see the converted one mode
network for a moment…
• What does this mean?
• What does 57 mean here?
Theresa had 57 connections
with others through
attending events.
Let’s do betweenness analysis with
converted one-mode data
• Let’s do the Freeman’s betwenness centrality
measure with converted event-by-event data
• What does this output mean?
• What does highest values of
betweenness mean here?
• Think about our previous
visualization!
Two mode network – Bipartite graph
• Let’s creating a bipartite graph with
“davis.##h data”
▫ Transform> Graph Theoretic> Bipartite …
Finally, we have a
square matrix
format!!!!
Two mode network – Bipartite graph
• Let’s do the Freeman’s degree centrality measure
with this bipartite graph
What does “14”
imply here?
What about “8” ?
Two mode network – Bipartite graph
• Let’s do the Bonacich power centrality measure
with this bipartite graph
• Q1: Which woman has the highest power?
• Q2: Which event has the highest power?
And Why?
Two mode network – Bipartite graph
• Let’s do the Bonacich power centrality measure
with this bipartite graph
• Q1: Which woman has the highest power?
• Q2: Which event has the highest power?
And Why?
• Theresa’s power centrality depends on
centralities of events where Theresa attended.
• E8 power centrality depends on centralities of its
members.
Two mode network data
• Let’s do the Core-periphery analysis with
“davis.##h” in UCINET
▫ Networks> 2-Mode Networks> 2-Mode
categorical core/periphery model
Core=A cluster of frequently co-occurring
actors & events
Periphery= (1) actors who are not co-occur to the
same events and (2) disjointed events because they
have no common actors.
0 =bad fit, 1 = excellent fit
Need your judgment..
Core=A cluster of frequently co-occurring
actors & events
Periphery= (1) actors who are not co-occur to the
same events and (2) disjointed events because they
have no common actors.
QAP(Quadratic Assignment Procedure)
• The basic idea of QAP is:
▫ To identify systematic connections between
different relations
Correlation
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Relation 1
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Causality
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QAP(Quadratic Assignment Procedure)
• In UCINET
▫ Tools> Testing Hypotheses> Dyadic (QAP) …
1. QAP correlation
2. Multiple regression QAP
1.QAP Correlations
• Computes the Pearson correlation all pairs of a set of
equally sized square matrices (With SAME actors!!)
• Then, assess the frequency of random measures as large
as actually observed.
• Basic question here: If two actors have a strong tie of one
type, are they also likely to have a strong tie of another?
• E.g., If Yoonie and Bill have a strong relation in their
friendship, do they also have a strong relation in money
exchange? What do you think? It might be an empirical
question… 
1.QAP Correlations
• So, we’d like to test whether or not these two (i.e.,
friendship and money exchange) relations are
positively related or randomly these relations are
observed.
• Algorithms of QAP:
▫ Calculate Pearson’s correlate coefficient between
corresponding cells of two matrices
▫ Randomly and repeatedly permute rows and columns
of two matrices to compute whether or not a random
measure is larger than or equal to the observed
relations between the matrices
1.QAP Correlations
• Let’s do some exercise.
• Here, we will test whether or not organizational
information sharing relations is positively
associated with monetary exchange relations.
• Data: Knoke & Wood (1978) collected 10
organizations’ two relationships: information
sharing (KNOKI) and monetary exchange
(KNOKE)
Result
correlation between the two matrices
Q: Information sharing is positively
related to money exchange here?
Result
Descriptive results from random 5000
permutations
Result
proportion of randomly generated
correlations that were as large (or small if they
are negatively correlated) as the observed
Simply, it is similar to p-value in statistics!
Wait! Here, what should be our null
Hypothesis?
Can we randomly observe this “correlation”
value (=-0.0508)?
1.QAP Correlations:
Another example- Trade data
• Let’s do another QAP correlation analysis!
• H: Crude materials trade relations between 24
countries will be positively associated with
manufactured goods trade relations between 24
countries.
• Data:
▫ CRUDE_MATERIALS
▫ MANUFACTURED_GOODS
• Analysis: QAP correlation in UCINET
2.Multiple Regression QAP
• Now, we’d like to focus on causality between
different types of relations, rather than
correlations.
• The independent variables should be the
matrices format with the SAME actors.
▫ E.g., different relations, attributes of the pairs in
the network
2.Multiple Regression QAP
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Independent Relation 2
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Independent Relation 1
Causality
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Dependent Relation
2.Multiple Regression QAP
• Example:
• Q: Political relations would be affected by
international trade. “Is diplomatic relations
affected by different types of trade relations
between countries?”
Trade relations
between
countries
Diplomatic relations
between countries
2.Multiple Regression QAP
• Data: Countries Trade Data
▫ Five types of relations
1.
2.
3.
4.
5.
MANUFACTURED_GOODS
FOODS
CRUDE_MATERIALS
MINERALS
DIPLOMATIC_EXCHANGE
Independent
VARs
Dependent VAR
2.Multiple Regression QAP
• Tools> Testing Hypotheses> Dyadic (QAP)>
MR-QAP Linear Regression> Double Dekker
Semi Partialling MRQAP
2.Multiple Regression QAP:
Another example- Friendship & Advice
• Data: Krackhardt (1987), five actors’ 1 friendship
and 3 types of advice networks
▫
▫
▫
▫
Krac_Friend_QAP = friendship network
Krac_Advice1_QAP = advice 1 network
Krac_Advice2_QAP = advice 2 network
Krac_Advice3_QAP = advice 3 network
• H: Friendship network will be positively affected
by different types of advice networks.
2.Multiple Regression QAP:
Application using attribute data
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Independent Relation 2
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Independent Relation 1
Causality
Dependent Relation
BUT!! Usually, it’s not easy to collect
multiple relational data with the same
actors. Are there any ways for us to use
this approach even if we have only one
relational data and some attribute data?
2.Multiple Regression QAP:
Application using attribute data
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Attribute 2
Causality
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Attribute 1
Dependent Relation
How about converting actors’
“attribute” into “matrix ” format?
Can we create similarity or dissimilarity matrix
between actors based on their attributes?
2.Multiple Regression QAP:
Application using attribute data
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Attribute 2
Causality
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Attribute 1
?? What does
“1” imply
here???
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Dependent Relation
How about converting actors’
“attribute” into “matrix ” format?
Can we create similarity or dissimilarity matrix
between actors based on their attributes?
2.Multiple Regression QAP:
Application using attribute data
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M3
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Attribute 2
Causality
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Attribute 1
E.g., 1 = M1 and M2
have same attribute
Dependent Relation
How about converting actors’
“attribute” into “matrix ” format?
Can we create similarity or dissimilarity matrix
between actors based on their attributes?
2.Multiple Regression QAP:
Application using attribute data
• Question to think:
▫ To what extent can advice network between
managers in a company be explained by their age,
length of service or tenure, level in the corporate
hierarchy and department?
2.Multiple Regression QAP:
Application using attribute data
• Data:
▫ Krackhardt D. (1987). collected network data from the 21
managers of a high-tech company on the west coast of the United
States. This company had just over 100 employees with 21
managers.
• 3 Networks = ADVICE, FRIENDSHIP, & REPORTS_TO
• 4 attributes of 21 managers
1. age (in years),
2. length of service or tenure (in years),
3. level in the corporate hierarchy (coded 1,2 and 3; 1=CEO, 2 =
Vice President, 3 = manager)
4. department (coded 1,2,3,4 with the CEO in department 0 ie not
in a department).
2.Multiple Regression QAP:
Application using attribute data
• Let’s check the dataset
▫ Networks
▫ Attributes
2.Multiple Regression QAP:
Application using attribute data
Age difference
relations
Tenure difference
relations
Advice network
Hierarchical Level
difference relations
Same department
relations
• Now, we will convert attribute data into matrix format
▫ Data> Convert Attribute to Matrix
How can we interpret this
result? What does it mean?
Employees with relatively short
tenure periods are going to those
with relatively long tenure periods
for advice
2.Multiple Regression QAP:
Application using attribute data
• Another example:
Age difference
relations
Tenure difference
relations
SAME Hierarchical
Level relations
Same department
relations
Friendship
network
• First, create SAME hierarchical level matrix by converting
attribute data into matrix format
▫ Data> Convert Attribute to Matrix
For more information...
• “QAP – the Quadratic Assignment Procedure”
(William Simpson, Harvard Business School,
2001).
• Decker, Krackhardt, Snijders, “Sensitivity of
MRQAP Tests to Collinearity and
Autocorrelation Conditions”