Transcript Collection of Network Data

Social Networks
Lecture 4:
Collection of Network Data
&
Calculation of Network
Characteristics
U. Matzat
1
Course design

Aim: knowledge about concepts in network
theory, and being able to apply them, in
particular in a context of innovation and alliances
-
-
Introduction: what are they, why important …
Small world networks
Four basic network arguments
Kinds of network data (collection) &
measurement
Business networks
Assignment 1
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Course outlook - today
4. Methods
-
-
Kinds of network data: collection (Part I)
Typical network concepts: calculation, UCINET
software, visualisation (Part II)
Later: Assignments
- complete network analysis
- ego-centered network analysis
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Part 1 – Collection of Network Data
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in traditional surveys a random sample of units (e.g.
managers) is interviewed
properties of individuals are correlated to analyze some
phenomena (e.g., correlation of age with openness for new
ideas)
focus on distributions of qualities of the individuals, not on
their relations
traditional assumption: sampled units (e.g., managers) are
independent of each other and not related to each other
inappropriate for SNA
traditional survey instruments had to be adjusted & new
ones had to be developed
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Collection of Network Data:
two main approaches within SNA
1.) ego-centered network analysis: network (of a specific
type) from the perspective of a single actor (ego)
2.) complete network analysis: the relations (of a specific
type) between all units of a social system are analyzed
-
-
-
the first approach rests on an extension of traditional survey
instruments
can be combined with random sampling
statistical data analyses possible with standard software
(e.g., SPSS)
the second approach is new
(usually) cannot be combined with random sampling
quantitative case study
statistical data analyses with specialized software (e.g.,
UCINET)
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Ego-centered network data
random sample:
selection of units (e.g. individuals) out of a population
inclusion of one individual does not influence whether
another one is also included
relationship between units is no criterion of selection
respondent (ego) mentions for a relationship of a certain
type (e.g. friendship relation) other individuals (alteri) with
whom he is related
usually the alteri are not within the sample
respondent gives additional information about
-some characteristics of the alteri (age etc.)
-the relations between the alteri
crucial: specialized items for the generation of alteri:
name-generator
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Ego-centered network data:
the generation of data via name generators
name generator for reconstruction of friendship networks in a general
population:
first step:
- "From time to time people discuss questions and personal problems that
keep them busy with others. When you think about the last 6 months - who
are the persons with whom you did discuss such questions that are of
personal importance for you.
Please mention only the first name of the individuals."
-
[If respondent mentions less than five names, ask once more:
"Anybody else? " Write down only the first five names.]
second step:-characterization of alteri (gender, age, etc) and relation
between ego and alteri (e.g., strength of relation)
third step:
-characterization of relation between the different pairs of alter
(e.g., strength of relation)
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Ego-centered network data:
example: reconstruction of university-company
relationships
- random sample of university researchers
- question of interest: how does a researcher’s network look
like that brings him into contact with business
representatives for collaboration?
- reconstruction of four parts of the network from the point of
view of the researcher:




within university- within own faculty
within university- outside own faculty
outside university – within business world
[outside university – personal friends, acquaintances etc.]
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example: reconstruction of university-company
relationships
Questionnaire items
Let us suppose that you are convinced that you have an idea, a
product or something similar, in which collaboration with a
business firm is a sensible and reasonable option.
Do you have any contacts that could be of substantial
value for bringing you in touch with a business firm?
0 yes
0 no (continue with question xx)
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example: reconstruction of university-company
relationships
From which of the employees within your faculty do you expect that
they can make a substantial contribution with respect to getting you
in contact with business firms that might become partners? Mention
the most important persons, at most four.
First name
Initial of last name
From which of the employees outside your faculty but within your
university do you expect that they can make a substantial
contribution with respect to getting you in contact with business firms
that might become partners? Mention the most important persons, at
most four.
First name
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Initial of last name
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Example (cont)
You mentioned up to 16 names of persons. Please write down the
name of the first person mentioned, the second person mentioned,
the third person mentioned, etc, until every name is on this list.
Make sure that each name is mentioned once and only once.
1.
..........................................................................
2.
..........................................................................
3.
..........................................................................
4.
..........................................................................
5.
..........................................................................
6.
..........................................................................
7.
..........................................................................
8.
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9.
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10.
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11.
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12
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13
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14
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15
..........................................................................
16.
..........................................................................
17.
..........................................................................
18.
..........................................................................
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Please carefully check this list. Are any
persons missing of whom you feel that
– given the questions – they should be
included in this list? Persons who are
crucial in getting cooperation between
you and a business partner going?
If yes, please add these persons to the
list (at most two extra persons) and
briefly describe your relation to this
person.
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Example (cont): second step
We would like to know how strong your relation with the persons in this
list is. A strong relation would be a relation with frequent contact
and with a regular exchange of information.
The relation is strong.
The relation is distant.
1.
Jack
○
○
2.
Jim
○
○
○
○
4.
○
○
5.
○
○
6.
○
○
7.
○
○
8.
○
○
9.
○
○
10.
○
○
11.
○
○
12
○
○
13
○
○
14
○
○
15
○
○
16.
○
○
17.
○
○
18.
○
○
3
. ….
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Example (cont): third step
Finally, we would like to ask you about the relations between the listed persons in
your network.
Start with the first person in the list. Consider the relation between this person and the other
persons in the list. Choose between:
S:
strong relation
D:
distant relation
0:
no relation
Fill out an X if you cannot judge the relationship.
Jim
Jack
...
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
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ego-centered network data: data matrix
example:
name generator for three best friends (of two respondents)
gender age
friend 1 existing?
friend 2 existing? friend 3 existing? tie strength 1
tie strength 1-2
gender friend 1
respondent 1
1
30
1
1
1
0.8
1
1
respondent 2
2
40
1
1
0
0.7
0
2
…………
…………
…………
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ego-centered network data: data matrix
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ego-centered network data: data matrix
- standard data matrix that can be analyzed with the
conventional techniques and conventional software (e.g.,
SPSS, STATA etc)
- but special type of variables of the data set
- some variables describe the respondent
- some variables describe the respondent's contacts
- some variables describe the relation between the
respondent and his contacts
- some variables describe relations between members of the
respondent's (primary) network
- these variables can be used to construct other variables that
describe properties of the respondent’s network (size, density
etc)
- you have to construct these variables: e.g. via “TRANSFORM –
COMPUTE” in SPSS
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ego-centered network data
-ego-centered network data necessary for testing of typical
network theories
-Example: structural holes hypothesis (ego=company)
-“Innovating companies tend to profit more from new
product ideas the more structural holes they have in their
collaboration networks with other companies.“
-a test of this hypothesis is impossible with traditional
surveys of companies
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ego-centered network data: Strengths and
weaknesses
+ random sampling possible
+ generalization to a well-defined population possible
+ for the social scientist easy to use techniques of data
analysis
- restriction to those parts of the network that are directly
visible to the respondent: the primary network; other
characteristics of the network are not taken into account
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ego-centered network data:
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ego-centered network data:
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complete network data:
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Complete network data
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example: network of informal communication between
employees of a project group consisting of 5 persons:
Mr Smith, Mr Jackson, Mr. White, Mrs Moneypenny, Mrs
Brown
questionnaire item for Mr Smith:
"With whom of the following persons do you now and then
chat during a normal working day?" Do you talk with…
Mr. Jackson
Mr. White
Mrs Moneypenny
Mrs Brown
0
0
0
0
yes
yes
yes
yes
0
0
0
0
no
no
no
no
question is presented to all members of the project group
you need to have a complete list of the names of all units
(e.g. individuals) of the social system (e.g. project group)
beforehand
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Complete network data: sociomatrix
Smith
Smith
Jackson
White
Moneypenny
Brown
Jackson White
1
1
0
1
1
1
1
0
0
1
1
1
0
0
1
Money- Brown
penny
1
0
0
0
1
1
1
0
0
1
-the data matrix is different from the traditional data matrix
-every cell ij in the matrix provides information about the relation
between units i and j ("from row i to column j")
-relation can be symmetric or asymmetric, valued or dichotomous
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Complete network data:
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collection of complete network data impossible for large
random samples
necessary for many hypotheses that make predictions about
structural effects:
"In groups with a high network density the diffusion of
innovations takes place more quickly than in groups with a
low density."
hypothesis can only be tested with complete network data
data matrix of complete network data cannot be analyzed
with the conventional data analysis techniques
specialized software that offers special techniques is needed
(e.g., UCINET)
you can calculate network characteristics of actors and of the
whole network
you can calculate network characteristics (within UCINET) for
actors that can be exported and then combined with other
data (e.g., SPSS data)
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Complete network data: Strengths and
weaknesses
+ all aspects of the structure of relationships between all
actors in a social system are taken into account
-
no random sampling, therefore no generalizations are
possible, rather: quantitative case study approach
- other techniques of data analysis necessary
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Complete network data:
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Part II: Calculation & visualisation of
network concepts (1): in- and outdegree
For complete, valued, directed network data with N actors, and
relations from actor i to actor j valued as rij , varying between 0
and R.
Centrality and power: outdegree (or: outdegree centrality)
For each actor j: the number of (valued) outgoing relations,
relative to the maximum possible (valued) outgoing relations.
OUTDEGREE(i) =
j r
ij
/ N.R
Centrality and power: indegree (or: indegree centrality)
same, but now consider only the incoming relations
NOTE1: this is a locally defined measure, that is, a measure that is defined for each actor separately
NOTE2: this gives rise to several global network measures, such as (in/out)degree variance
NOTE3: if your network is not directed, indegree and outdegree are the same and called degree
NOTE4: these measures can be constructed in SPSS; no need for special purpose software. Try this
yourself!
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Network measures (2):
number of ties of a certain quality
1
2
3
4
5
=
=
=
=
=
I
I
I
I
I
do not know who this is
know who it is, but never talked to him/her
have spoken to this person once or twice
talk to this person regularly
talk to this person often
Number of ties:
For each network or for each actor, the number of ties above
a certain threshold
(say, all ties with a value above 3)
Number of weak ties (remember Mark Granovetter?):
For each network or for each actor, the number of ties above
and below a certain threshold
(say, only ties with values 2 and 3)
Try creating this one yourself in SPSS (try using ‘recode’)
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Network measures (3): closeness
Centrality and power again: closeness
= Average distance to all others in the network
Note: a shortest path from i to j is called a “geodesic”
Define distance Dij from i to j as:
* Minimum value of a path from i to j
For every actor i, average distance =
j D
ij
/N
NOTE: THIS IS NOT EASY TO DO ANYMORE IN SPSS!
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Network measures (4): the most common
global network property
Density
(J. Coleman: “Dense networks provide social capital.”)
For each network: the number of (valued) relations, relative to the
maximum possible number of (valued) relations.
=
i,j r
ij
/ N (N-1) R
(directed, valued ties)
NOTE:
normally only of use if your data consist of multiple networks
(alliance networks in different sectors or countries / friendship
networks in school classes / …)
NOTE:
this is still doable in SPSS
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Network measures (5): Subgroup
Models (Cohesion)
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aim: description of cohesive subgroups within the larger
network
general and common idea: a subgroup has a certain degree
of cohesiveness (direct ties, strong ties)
can also be used to make predictions about the diffusion of
innovations according to the cohesion model (which pairs of
actors influence each other?)
- which companies constitute a subgroup within the
network?
- which companies are in many subgroups?
- how many subgroups do exist?
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Subgroups: Some general terminology you
need to know…..
-
reachability
if a path exists between 2 nodes then these nodes are called
reachable
path length
number of lines of a path (dichotomous data)
-
example: path length 4213 = 3
-
geodesic distance between two nodes
-
there can be more than one path between two nodes, the
different paths can have different lengths
d(i,j)=length of the shortest path between two nodes i and j
example: 4213 = 3 , d(i,j)=3 if there exists no shorter
path between i and j
d(i,j)=
if i,j are not reachable
8
-
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Subgroups: Terminology....
-
-
-
8
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completeness of a graph
a graph is complete if all pairs of nodes (i,j) are reachable
with d(i,j)=1
connectedness
a graph is connected if for every pair (i,j) d(i,j)<
subgraphs
a subgraph Gs consists of a subset NsN and its lines Ls L
that connect all {i,j}  Ns
Maximality
a subgraph is maximal with respect to some property (e.g.,
maximal with regard to completeness) if that property holds
for the subgraph, but does no longer hold if any additional
node and the lines incident with the node are added
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Subgroups example:
maximal completeness
5
1
7
6
2
4
3
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maximal complete subgraph Gs
Ns={1,2,3,4,5} and the ties between
them
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Subgroup Definitions for undirected
dichotomous ties
Cliques
a cliques is a maximal complete subgraph that consists of at least
three nodes
2
7
1
3
4
Which cliques? 5
6
{1,2,3}, {1,3,5}, {3,4,5,6}
cliques can overlap, a clique can not be part of a larger clique because of the
maximality condition
impossible to calculate with SPSS!
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This was covered in the 3rd lecture
Network measures (6):
Ron Burt: “Structural holes
Structural holes
create value”
A
1
B
7
3
2
James
Robert
6
Robert will do better than
5
4
8
James, because of:
-informational benefits
C
-“tertius gaudens” (entrepreneur)
-autonomy
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Network measures (6):
Structural holes
- Burt, R.S. (1995)
- NOTE: structural holes can be defined on egonetworks!
Burt splits his structural holes measure in four separate ones:
-
[1] effective size
-
[2] efficiency (= effective size / total size)
-
[3] constraint (degree to which ego invests in alters
who themselves invest in other alters of ego)
-
[4] hierarchy (adjustment of constraint, dealing with
the degree to which constraint on ego is
concentrated in a single actor)
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Structural holes: Effective size & efficiency
A
B
We calculate effective
size and efficiency
for actor G
F
E
G
(note: because this is an
ego-network, all would be
different if we would have
chosen, for instance,
actor A)
D
C
Ego=G,
Size[G]=6
redundancy
A
B
3/6 2/6
C
D
0/6
1/6
E
F
1/6 1/6
Eff.
size
Efficiency
4.67
78%
Or, the same but a bit easier: Effective size = size - average
degree of ego’s alters in ego’s network (excluding ties to ego).
Here:
6 - {3 (A) + 2(B) + 0(C) + 1(D) + 1(E) + 1(F)}/6 = 6 - 1.33 = 4.67
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Defining constraint:
actors must divide their attention
A
B
F
E
G
D
A
A
B
C
D
E
F
G
0.25
0
0
0.25
0.25
0.25
0.0
0.33
0
0
0.33
0
0
0
1.00
0
0
0.50
0
0.50
B
0.33
C
0
0
D
0
0.50
0
E
0.50
0
0
0
F
0.50
0
0
0
0
G
0.17
0.17
0.17
0.17
0.17
0.50
0.17
C
The assumption is that actors can only invest a certain amount of
time and energy in their contacts, and must divide the available time
and energy across contacts.
If not explicitly measured, we assume all contacts are invested in
equally.
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Constraint
Actor i is constrained in his relation
with j to the extent that:
[a] i invests in another contact q
who …
q
piq
i
pqj
pij
[b] invests in i’s contact j
j
Total investment of i in j =
Pij + q (piq pqj)
“Since this also equals i’s lack of
structural holes, constraint
of i in j is taken to equal”
( Pij + q (piq pqj) )2
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Calculating constraint using matrices (1)
Adjacency matrix
c1
c2
c3
c4
c5
c6
c7
r1
0
.25
0
0
.25
.25
.25
r2
.333
0
0
.333
0
0
.333
r3
0
0
0
0
0
0
1
r4
0
.5
0
0
0
0
.5
r5
.5
0
0
0
0
0
.5
r6
.5
0
0
0
0
0
.5
r7
.17
.17
.17
.17
.17
.17
0
c1
c2
c3
c4
c5
c6
c7
r1
.37575
.0425
.0425
.12575
.0425
.0425
.33325
r2
.05661
.30636
.05661
.05661
.13986
.13986
.24975
r3
.17
.17
.17
.17
.17
.17
0
r4
.2515
.085
.085
.2515
.085
.085
.1665
r5
.085
.21
.085
.085
.21
.21
.125
r6
.085
.21
.085
.085
.21
.21
.125
r7
.22661
.1275
0
.05661
.0425
.0425
.52411
P=
(see two slides ago) all
investment from i in j in 1
step
Matrix product
P2 = P*P =
all investments from i in j in 2
steps
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Calculating constraint using matrices (2)
c1
c2
c3
c4
c5
c6
c7
r1
.37
.29
.04
.12
.29
.29
.58
r2
.38
.30
.05
.38
.13
.13
.58
r3
.17
.17
.17
.17
.17
.17
1
All investments from i to j in
1 or 2 steps
R4
.25
.58
.08
.25
.08
.08
.66
r5
.58
.21
.08
.08
.21
.21
.62
Pij + q (piq pqj)
r6
.58
.21
.08
.08
.21
.21
.62
r7
.39
.29
.17
.22
.21
.21
.52
P+
P2
=
(0.666)2
= 0.444
c1
c2
c3
c4
c5
c6
c7
r1
.141
.085
.002
.015
.085
.085
.340
Hadamard matrix
r2
.151
.093
.003
.151
.019
.019
.339
product
r3
.028
.028
.028
.028
.028
.028
r4
.063
.342
.007
.063
.007
.007
.444
r5
.342
.044
.007
.007
.044
.044
.390
r6
.342
.044
.007
.007
.044
.044
.390
r7
.157
.088
.028
.051
.045
.045
.274
(P+P2)2h
= P+P2 squared element wise
Constraint(i,j) can be read
from this matrix
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Etc …
1
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Calculating constraint using matrices (3)
Total constraint for actor i =
sum of all constraints Cij with ji
c1
c2
c3
c4
c5
c6
c7
r1
.141
.085
.002
.015
.085
.085
.340
= 0.755 <- Constraint(1)
r2
.151
.093
.003
.151
.019
.019
.339
= 0.779 <- Constraint(2)
r3
.028
.028
.028
.028
.028
.028
r4
.063
.342
.007
.063
.007
.007
.444
= 0.934 <- Constraint(4)
r5
.342
.044
.007
.007
.044
.044
.390
= 0.879 <- Constraint(5)
r6
.342
.044
.007
.007
.044
.044
.390
= 0.879 <- Constraint(6)
r7
.157
.088
.028
.051
.045
.045
.274
= 0.691 <- Constraint(7)
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= 1.173 <- Constraint(3)
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Hierarchy
-
= degree to which constraint is concentrated in a single actor
-
Cij = constraint from j on i
-
-
-
(as on previous pages)
N = number of contacts in i’s network
C = sum of constraints across all N relationships
Hierarchy (i)
 Cij   Cij 
j  C N  ln C N 

N ln( N )
Minimum = 0 (all i’s constraints are the same)
Maximum = 1 (all i’s constraint is concentrated in a single contact)
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Network concepts: Ucinet Software
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Network concepts: Ucinet Software
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Network concepts: Ucinet Software
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Network concepts: Ucinet Software
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Network concepts: Ucinet Software
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Network concepts: Ucinet Software
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Network concepts: Ucinet Software
Social Networks, TU/e - 0ZM05/0EM15/0A150
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Network concepts: Ucinet Software
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Network concepts: Ucinet Software
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To Do:

Read the chapters 6, 9, 10-11 of Hanneman &
Ridle on network techniques

Download/install Ucinet and the talk.dl data

Try it out!

(Install SPSS and fresh up your SPSS knowledge!)
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