Social Networks Lecture 4: Collection of Network Data

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Social NetworksLecture 4Collection of
Network DataCalculation of Network
CharacteristicsU. Matzat
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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

• 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 researchers
  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 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. ..........................................................................
9. ..........................................................................
10. ..........................................................................
11. ..........................................................................
12 ..........................................................................
13 ..........................................................................
14 ..........................................................................
15 ..........................................................................
16. ..........................................................................
17. ..........................................................................
18. ..........................................................................

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.
Jack ? ?
2. Jim ? ?
3 . . ? ?
4. ? ?
5. ? ?
6. ? ?
7. ? ?
8. ? ?
9. ? ?
10. ? ?
11. ? ?
12 ? ?
13 ? ?
14 ? ?
15 ? ?
16. ? ?
17. ? ?
18. ? ?

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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 Jim Jim Jim Jim Jim Jim Jim Jim Jim Jim Jim Jim Jim Jim Jim Jim 01
Jack Jack Jack Jack Jack Jack Jack Jack Jack Jack Jack Jack Jack Jack Jack Jack 02
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... 03
04
05
06
07
08
09
10
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12
13
14
15
16
17
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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
  respondents 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
  (egocompany)
• 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

• 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 0 yes 0 no Mr. White 0
  yes 0 no Mrs Moneypenny 0 yes 0
  no Mrs Brown 0 yes 0 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

• 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

• 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 rij / 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 I do not know who this is
• 2 I know who it is, but never talked to him/her
• 3 I have spoken to this person once or twice
• 4 I talk to this person regularly
• 5 I 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 Dij / 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 rij / 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)

• 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

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Subgroups Terminology....

• 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)lt
• 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
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maximal complete subgraph Gs Ns1,2,3,4,5 and
the ties between them
1
6
2
4
3
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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
•  
•  
•  
•                 5     
  6
•  

Which cliques?
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 conditionimpossible to
calculate with SPSS!
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Network measures (6) Structural holes
This was covered in the 3rd lecture
Ron Burt Structural holes create value
A
1
B
7
3
2
James
Robert
4
5
6

• Robert will do better than
• James, because of
• informational benefits
• tertius gaudens (entrepreneur)
• autonomy

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C
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Network measures (6) Structural holes

• Burt, R.S. (1995)
• NOTE structural holes can be defined on
  ego-networks!
• 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
We calculate effective size and efficiency for
actor G (note because this is an ego-network,
all would be different if we would have chosen,
for instance, actor A)
EgoG, SizeG6 A B C D E F Eff. size Efficiency
redundancy 3/6 2/6 0/6 1/6 1/6 1/6 4.67 78
Or, the same but a bit easier Effective size
size - average degree of egos alters in egos
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

• 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
• b invests in is contact j
• Total investment of i in j
• Pij ?q (piq pqj)
• Since this also equals is lack of
• structural holes, constraint
• of i in j is taken to equal
• ( Pij ?q (piq pqj) )2

q
piq
pqj
i
j
pij
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Calculating constraint using matrices (1)
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
Adjacency matrix P (see two slides ago) all
investment from i in j in 1 step
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
Matrix product P2 PP 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 R4 .25 .58 .08 .25
.08 .08 .66 r5 .58 .21 .08 .08 .21
.21 .62 r6 .58 .21 .08 .08 .21 .21
.62 r7 .39 .29 .17 .22 .21 .21 .52
P P2 All investments from i to j in 1 or 2
steps Pij ?q (piq pqj)
(0.666)2 0.444 Etc
c1 c2 c3 c4 c5 c6 c7 r1
.141 .085 .002 .015 .085 .085 .340 r2 .151
.093 .003 .151 .019 .019 .339 r3 .028
.028 .028 .028 .028 .028 1 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
Hadamard matrix product (PP2)2h PP2 squared
element wise Constraint(i,j) can be read from
this matrix
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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 r2 .151
.093 .003 .151 .019 .019 .339 r3 .028
.028 .028 .028 .028 .028 1 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
0.755 lt- Constraint(1) 0.779 lt-
Constraint(2) 1.173 lt- Constraint(3) 0.934 lt-
Constraint(4) 0.879 lt- Constraint(5) 0.879 lt-
Constraint(6) 0.691 lt- Constraint(7)
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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 is network
• C sum of constraints across all N relationships
• Hierarchy (i)
• Minimum 0 (all is constraints are the same)
• Maximum 1 (all is 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
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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!)