Transcript Document

Social network analysis
Chris Snijders
Dept of Technology Management
Cap. group Technology & Policy
Eindhoven University of Technology
Eindhoven, The Netherlands
[email protected]
[note: material partly collected online!]
Social network analysis – introduction and some key issues
Program
9:00 – 12:30 and 13:30 – 17:00:
- 09:00 – 09:15: A brief inventory
- 09:15 – 10:30: Introduction to social network analysis and
social capital theory,
typical research questions
- 10:30 – 10:45: <break>
- 10:45 – 12:30: Some classic social network studies
- 12:30 – 13:30: <Lunch>
- 13:30 – 14:30: Network concepts and network measurements
- 14:30 – 15:15: Dealing with network analysis
- 15:15 – 15:30: <break>
- 15:30 – 16:15: A brief look on network analysis software
- 16:15 – 17:00: Leftovers / assignment
- …
Note: slides will be available online later
Social network analysis – introduction and some key issues
Brief introduction to
social network analysis
Social network analysis – introduction and some key issues
We live in a 'social space'
"If we ever get to the point of
charting a whole city or a whole
nation, we would have … a picture of a
vast solar system of intangible
structures, powerfully influencing
conduct, as gravitation does in space.
Such an invisible structure underlies
society and has its influence in
determining the conduct of society as
a whole."
Jacob L. Moreno
New York Times, April 13, 1933
Social network analysis – introduction and some key issues
We live in a connected world
“To speak of social life is to speak
of the association between people –
their associating in work and in play,
in love and in war, to trade or to
worship, to help or to hinder. It is
in the social relations men establish
that their interests find expression
and their desires become realized.”
Peter M. Blau
Exchange and Power in Social
Life, 1964
Social network analysis – introduction and some key issues
Social network analysis – introduction and some key issues
Example network
(source: Borgatti)
Social network analysis – introduction and some key issues
Example network: a food “chain”
Social network analysis – introduction and some key issues
Why do networks matter?
Social network analysis – introduction and some key issues
Why do networks matter?
Social network analysis – introduction and some key issues
“practical classics”
Social network analysis – introduction and some key issues
The network perspective
Two firms in the same market.
Which firm performs better (say, is more innovative):
A or B?
A
B
This depends on:
•Cost effectiveness
•Organizational structure
•Corporate culture
•Flexibility
•Supply chain management
•…
Social network analysis – introduction and some key issues
The network perspective
Two firms in the same market.
Which firm performs better (say, more innovative): A or B?
Note
A
B
Networks are one specific
way of dealing with “market
imperfection”
AND … POSITION IN THE NETWORK OF FIRMS
Social network analysis – introduction and some key issues
Origins of social network research
Main development in social sciences in the 30’s.
Psychology
• sociometry and sociograms (Moreno)
• groups interact with their environment (Lewin) ->
suggestion to use vector theory and topology to model
this
• “balance theory” (Heider)
Anthropology
• E.g., Hawthorne experiments (Mayo)
• 50’s: conflicts in groups (Barnes, Bott, White)
And: mathematics has been working on “points and
lines” (graph theory) for a long time.
Social network analysis – introduction and some key issues
Increasing popularity
Social network analysis – introduction and some key issues
Social network researchers congregate at the
Sunbelt Conference
• Informal conferences in mid-late 1970s
– Toronto (1974); Hawaii
• Formalized as Sunbelt 1981 – annual
• Normal Rotation: SE US, US West, Europe
– Slovenia (2004); Charleston (Feb 2005), Vancouver?
Social network analysis – introduction and some key issues
The International Network of Social Network Analysis (INSNA)
• Founded by Barry Wellman in 1976-1977
– Sabbatical Travel Carried Tales
– Nick Mullins: Every “Theory Group” Has an Organizational Leader
– Owned by Wellman until 1988 as small business
• Subsequent Coordinators/Presidents
– Al Wolfe, Steve Borgatti, Martin Everett
• Steering Committee
• Non-Profit Constitution under Borgatti; Coordinator > President
– Bill Richards President, 2003• Scott Feld VP; Katie Faust Treasurer; Frans Stokman, Euro. Rep.
• Our First Real Election
• Grown from 175 to 400 Members
• Many More on Listserv (Not Limited to Members)
– Steve Borgatti maintains; unmoderated
• Website: www.insna.org
The socnet-mailing list
*****
To join INSNA, visit http://www.insna.org
*****
Dear all,
Last week I asked about designing a survey form to gather SNA data
inside a consulting firm. I received many useful bits of
information
including examples of survey forms, references to articles and also
a full text dissertation about the issue. I want to thank everyone
who shared their wisdom about this. Please find below the advice I
received. I hope this helps somebody else also. With best regards,
Anssi Smedlund
 see answer
Social network analysis – introduction and some key issues
Dedicated social network journals
• Wellman founded,edited,published Connections, 1977
– Informal journal: “Useful” articles, news, gossip,
grants, abstracts, book summaries
– Bill Richards, Tom Valente edit now
• Lin Freeman founded, edits Social Networks, 1978?
– Formal journal: Refereed articles
– Ronald Breiger now co-editor
• David Krackhardt founded, edits the Journal of
Social Structure, 2000?
– Online, Refereed
– Lots of visuals
– Articles Appear Occasionally when their time has come
Social network analysis – introduction and some key issues
Some key social network books
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13)
Elizabeth Bott, Family & Social Network, 1957
J. Clyde Mitchell, Networks, Norms & Institutions, 1973
Holland & Leinhardt, Perspectives on Social Network
Research,1979s
S. D. Berkowitz, An Introduction to Structural Analysis, 1982
Knoke & Kuklinski, Network Analysis, 1983, Sage, low-cost
Charles Tilly, Big Structures, Large Processes, Huge
Comparisons, 1984
Wellman & Berkowitz, eds., Social Structures, 1988
David Knoke, Political Networks, 1990
John Scott, Social Network Analysis, 1991
Ron Burt, Structural Holes, 1992
Manuel Castells, The Rise of Network Society, 1996, 2000
Wasserman & Faust, Social Network Analysis, 1992
Nan Lin, Social Capital (monograph & reader), 2001
Social network software
1)
UCINet – Many things on network analysis
1)
2)
Lin Freeman, Steve Borgatti, Martin Everett
MultiNet – Whole Network Analysis
1)
+ Nodal Characteristics
3)
Structure – Ron Burt – No longer maintained
4)
P*Star – Dyadic Analysis – Stan Wasserman
5)
Krackplot – Network Visualization (Obsolete)
1)
David Krackhardt, Jim Blythe
6)
Pajek – Network Visualization – Supersedes Krackplot
7)
StocNet – Tom Snijders - collected programs for, e.g., analysis of
dynamic networks
Kinds of data collection through SNA history
•
Small Group “Sociometry”1930s > (Moreno, Bonacich, Cook)
–
–
•
Ethnographic Studies, 1950s > (Mitchell, Barnes)
–
•
Organizational, Inter-Organizational, Inter-National Analyses
Political Structures, 1970s > (Tilly, Wallerstein)
–
–
•
Formalist / Methods & Substantive Analysis
Survey & Archival Research, Whole Nets, 1970s >
–
•
Community, Support & Social Capital, “Guanxi”
Mathematics & Simulation, 1970s > (Freeman, White)
–
•
Does Modernization > Disconnection?
Survey Research: Personal Networks, 1970s >
–
•
Finding People Who Enjoy Working Together
Evolved into Exchange Theory, Small Group Studies
Social Movements, Mobilization (anti Alienation)
World Systems (asymmetric structure > Globalization)
Computer Networks as Social Networks, late 1990s > (Sack)
–
Automated Data Collection
The basics: what is a network
Network
A set of ties among a set of actors
(or “nodes”)
Actors
persons, organizations, business-units,
countries …
Ties
Any instance of ‘connection of interest’
between the actors
Social network analysis – introduction and some key issues
Example: kinds of relations among persons
The content of ties matters
Some examples
• Kinship
– Mother
– Has bloodband to
• “Role based”
– Boss of
– Friend of
• Communication, perception
– Talks to
– Knows (of)
• Affection
– Trusts
– Likes, loves
• Interaction
– Gives advice to
– Gets advice from
– Has sex with
• Affiliation
– Belongs to same group/club
– Part of the same (business)
unit
Social network analysis – introduction and some key issues
Example: relations among organizations
Firms as actors
Firm members as actors
• Buys from, sells to,
outsources to
• Has done business with
• Owns shares of, is part of
• Has a joint venture or
alliance with, has sales
agreements with
• Has had quarrels with
• Has a personal friend in
board of
• Has a personnel flow to
• Have an interlocking board
Social network analysis – introduction and some key issues
Example network: Collaboration between disciplines
(source: Borgatti)
Social network analysis – introduction and some key issues
Example network: terrorists
(source: Borgatti)
Social network analysis – introduction and some key issues
The network perspective (“structuralism”)
Relations between actors vs actor attributes
• Individual characteristics are not the only thing that
counts, because …
• actors influence each other
• Actors act on the basis of information that flows to them
through relations between actors
Structuralism (vs individualism):
an emphasis on social capital
• Explanation does not reside in actors, but in the
connections between them
• A different belief on social capital vs human capital
– Social capital beats human capital (the real structuralists)
– Social capital determines the extent to which your potential
human capital can materialize (an interaction effect – see
Burt’s Structural Holes book)
– Human capital beats social capital (the real individualist)
 at least, consider how social capital can be of influence
Social network analysis – introduction and some key issues
Some typical research questions in
social network analysis
Social network analysis – introduction and some key issues
Networks = Y
or
Networks = X
In most social science applications, networks are considered
as an independent variable.
For instance
Firm A performs better than B because firm A is embedded in
a network with a lot of ties (a network of higher “density”)
or
Person A performs better than B because person A has a lot
of ties to other persons and person B doesn’t
(firm A has a higher “outdegree”)
Social network analysis – introduction and some key issues
Networks = Y
or
Networks = X
Sometimes: networks as the dependent variable
For instance:
How do the social networks of successful
people/firms/… differ from the social networks of
others? (and why is that?)
And, on rare occasions: dynamic network theory
For instance:
How do the friendship networks of people change over
time? Or: how do the alliance networks of firms change
over time?
Social network analysis – introduction and some key issues
Or: the tie itself as the dependent variable
Homophily
– Having one or more
common social
characteristics
– The larger the
homophily, the more
likely it is that two
nodes will be connected
Propinquity
– Nodes are more likely
to be connected with on
another if they are
geographically near to
on another.




Resource complementarity
– Resources are
‘strenghts’ or tangible
and intangeble assets
of actors
Social network analysis – introduction and some key issues
Using network arguments
• Make sure that you define the actors/nodes, and what
the ties between them represent (directed?,
weighted?).
• Make clear how and what (kind of) network
characteristics drive your result. There are so many
network characteristics … think hard!
• Don’t forget … shop around for arguments in areas
unrelated to your own! (where perhaps only the nodes
and the ties are different!)
“The best ideas already exist. You do not have to
create them, you only have to find them.”
Social network analysis – introduction and some key issues
Kinds of network arguments (from: Burt)
• Closure competitive advantage stems from managing risk;
closed networks enhance communication and enforcement of
sanctions
• Brokerage competitive advantage stems from managing
information access and control; networks that span
structural holes provide the better opportunities
• Contagion information is not a clear guide to behavior, so
observable behavior of others is taken as a signal of proper
behavior.
[1] contagion by cohesion: you imitate the behavior of those you
are connected to
[2] contagion by equivalence: you imitate the behavior of those
others who are in a structurally equivalent position
• Prominence information is not a clear guide to behavior, so
the prominence of an individual or group is taken as a
signal of quality
Social network analysis – introduction and some key issues
Typical social network research questions
• How is property X of an actor related to his or her
social network properties?
X
job success
well-being
longeveity
innovativeness
…
actor type
individual
individual
individual
firm
…
network char.
structural holes
outdegree
freq. of contacts
closure
…
Social network analysis – introduction and some key issues
Network concepts
Social network analysis – introduction and some key issues
Kinds of ties
Directed vs undirected
Undirected ties (lines)
• A is in a joint
venture with B
• A is in the same
market as B
Directed ties (arrows)
• A owns B
• A has bought something
from B
B
A
B
A
Social network analysis – introduction and some key issues
Valued ties
Ties can have a value
attached
- Strength of relation
- Information capacity
of tie
- Rates of traffic
- Distance between nodes
- Probabilities of
passing information
- Frequency of
interaction
- …
4
2
1
8
2
5
1
Social network analysis – introduction and some key issues
Network representations: graph and matrix
A 1-mode, non-valued, directed network
A
B
C
D
A
-
1
1
0
B
0
-
0
0
C
0
1
-
1
D
0
0
0
-
A
B
C
D
A 1-mode, non-valued, undirected network
A
B
C
D
A
-
9
4
0
B
9
-
1
0
C
4
1
-
3
D
0
0
3
-
A
4
C
9
B
3
D
1
Social network analysis – introduction and some key issues
Kinds of network data
AND another dimension: directed relations or undirected
Social network analysis – introduction and some key issues
Formal methods in network theory
Visual Mapping (Euclidean / Topology)
From Sociograms (1934) to 3D Maps (Today)
Graph Theory
Network G = (N actors, L Links, V Values); Directed
Graphs, Undirected Graphs, Valued Graphs
Matrix algebra / sociometry
Algebraic manipulations correspond to network
characteristics. N actors (n1, n2, n3 …. n n) ; M actors (m1,
m2, m3 …. mm); Matrix Notation: x ijr = value of the tie from
ni to mj, on the relation Xr
Statistics?
Social network analysis – introduction and some key issues
Some network concepts
X
Walk
E
C
gets from A to X:
F
A-C-A-D-F-X
D
A
Trail
Walk, but without
repeating lines:
B
Distance between A and X
A-D-E-F-D-B-X
Length of shortest path
(“geodesic distance”)
Path
Connected graph
Walk, but without
repeating nodes:
For any couple of nodes
there exists a path from one
to the other
A-D-E-F-X
Social network analysis – introduction and some key issues
More network concepts
X
Cutpoints
E
C
Nodes which, if deleted,
would disconnect the
network.
For instance, node “D”.
F
D
A
B
Bridges
Ties which, if deleted,
would disconnect the
network.
For instance, the tie
between A and D.
Social network analysis – introduction and some key issues
Individual Network Measures
• Degree: Percentage of ties to the other actors an
actor has (in directed graphs: InDegree and OutDegree)
• Degree quality: Percentages of ties
to other actors the neighbors
of an actor have
A
B
C
D
A
-
1
1
0
B
0
-
0
0
C
0
1
-
1
D
0
0
0
-
• Local density (=lack of structural holes): Extent to
which neighbors of an actor are connected
• Betweenness: extent to which pairs of actors depend on
the focal actor to “communicate”
• Closeness: the average minimal distance to other
actors in the network
Social network analysis – introduction and some key issues
Global Network Measures
• Network size: Number of actors
• Density: Percentage of ties present in the network
• Centralization: Concentration of ties on limited
number of actors in the network (e.g., degree
variance. In general, any individual measure implies a
global measure)
• Transitivity: tendency of triads to be closed (how
often is it the case that if i->j and j->k, then also
i->k?)
Social network analysis – introduction and some key issues
About network literature
Social network analysis – introduction and some key issues
Make sure you talk about network embeddedness
Single actor
properties
determine
behavior
Dyad
+ properties of
partner and
relation
determine
behavior
Network
+ network
properties
determine
behavior
Temporal
embeddedness
Network
embeddedness
Social network analysis – introduction and some key issues
About social network literature
• Networks are not new (from thirties), but applications
of some rigor are only from the beginning of the
eighties.
• Networks are about connections between actors, even
about the connections beyond the connections of focal
actors.
• “Networks” and “social capital” are often used in the
same context
• Only about now, the real potential of network
arguments can be unleashed because of adequate
software. Making smart use of internet related
possibilities seems promising.
Social network analysis – introduction and some key issues
A remark on social network analysis and
internet research
• The prevalence of Internet use shifts questions
related to social capital from “neighborhood research”
to “Internet Research”
• Through Internet, it is possible to have connections
(“ties”) with persons and institutions you could
otherwise never reach
• Social network data collection has become less
difficult:
– Through log-files of on-line behavior
– Because of measurement of social networks through the
Internet
– Because of invasive methods (“spyware”) of data
collection
Social network analysis – introduction and some key issues
Social Network Analysis and Internet Research
Internet Research [1]: research on a non-internet
topic, but collected by internet means
(e.g., a general social survey)
Internet Research [2]: research on typical Internet
topics:
-
online knowledge sharing
online support groups
online user communities
online game communities
online reputation networks
email circles
use of msn etc
Social network analysis – introduction and some key issues
Research classic:
Granovetter’s (1973)
“Strength of weak ties” as a
precursor to Burt’s structural
holes
Social network analysis – introduction and some key issues
Mark Granovetter:
The strength of weak ties
• Dept of Sociology, Harvard
• The strength of weak ties (1973)
• Granovetter was a sociology graduate student;
interviewed about 100 people who had changed jobs in
the Boston area.
• More than half of the people found their new job
through personal contacts (already at odds with
standard economics).
• Many of these contacts were rather indirect (a “weak
tie”)
• This is surprising, because “strong ties” are usually
more willing to help you out
• Granovetter’s conjecture: your strong ties are more
likely to contain information you already know
• According to Granovetter: you need a network that is
low on transitivity
Social network analysis – introduction and some key issues
Mark Granovetter:The
strength of weak ties revisited
• You need weak ties because they give you better access
to information
• Coser (1975) You need bridging weak ties: weak ties
that connect to groups outside your own clique (+ you
need cognitive flexibility, because you need to cope
with heterogeneity of ties)
Empirical evidence:
• Granovetter (1974)
28% found job through weak ties
17% found job through strong ties
• Langlois (1977) showed this result depends on the kind
of job
• Blau: argument about high status people connecting to
a more diverse set of people than low status people
• … see Granovetter’s paper
Social network analysis – introduction and some key issues
Mark Granovetter:other work
Granovetter is well known for the notion of
“(social) embeddedness”:
all behavior occurs in a social structure, and that structure
has
influence on behavior.
Institutional embeddedness:
shared rules and norms
example: two firms in an alliance, working under different judicial systems
Temporal embeddedness:
the existence of past relations and anticipated future
relations.
example: two firms in an alliance who have worked together before, vs not
example: two firms in an alliance who anticipate future dealings, vs not
Structural embeddedness:
the existence of relations with third parties
example: two firms in an alliance have mutual customers, vs not
Social network analysis – introduction and some key issues
From weak ties to structural holes (Burt)
• “Weak ties connect to heterogenous information”
implies that actually the argument is not so much
about the weakness of ties …
• … but about whether or not you connect to heterogenous
information (the “effective size” of your network)
Burt: structural holes
A has structural holes
to the extent that he
connects others that are
not connected
themselves.
A
B
Here: A has more than B
Social network analysis – introduction and some key issues
Research classic:
Burt’s (1988)
“Structural holes” as a response
to Coleman’s closure argument
Social network analysis – introduction and some key issues
Ron Burt:Structural
holes versus network closure as social capital
Burt’s conclusion:
structural holes beat network closure
when it comes to predicting which actor
performs best
Coleman says closure is good
• Because information goes around fast …
• … and it facilitates trust
[fear of a damaged reputation
precludes opportunistic behavior]
University of Chicago
graduate school of
business
He subsequently compares people with
dense networks with those with
networks rich in “structural holes”
Social network analysis – introduction and some key issues
Social organization
“Structural holes create value”
A
B
1
7
3
2
James
Robert
5
6
4
Robert will do better than James,
because of:
-informational benefits
C
-“tertius gaudens” (entrepreneur)
Social network analysis – introduction and some key issues
Structural holes / Redundancy
At this point it is not that clear yet what precisely
constitutes a structural hole.
Burt does define two kinds of redundancy in a network:
• Cohesion: two of your contacts have a close connection
• Structurally equivalent contacts: contacts who link to
the same third parties
This more or less corresponds to (the inverse of)
structural holes:
• If two of your contacts are connected, you do not
connect a structural hole
• If two of your contacts lead to the same other, then
your are not the only one bridging a structural hole
Social network analysis – introduction and some key issues
Structural holes vs network closure
Empirical evidence on
Dependent variable
= early promotion
= large bonus
= outstanding evaluation
all seem to favor Burt’s structural holes
Burt on Coleman:
– Coleman’s dependent variable = “dropping out of school”
– parents in a close network will earn less
And about network closure:
Best team performance when groups are cohesive but team
members have diverse external contacts.
Social network analysis – introduction and some key issues
Structural holes vs network closure
• Coleman:
closure can overcome trust and cooperation problems
(empirical evidence from data on school dropouts)
• Burt:
Structural holes give entrepreneurial possibilities
(empirical evidence from data on US managers)
Perhaps this is not so much a controversy after all …?
Social network analysis – introduction and some key issues
Research classic:
The “small world phenomenon” and
theoretical research into social
networks
Or: one typical kind of network
structure
Social network analysis – introduction and some key issues
The small world phenomenon – Milgram (1967)
• Milgram sent packages to a couple hundred people in
Nebraska and Kansas.
• Aim was “get this package to <address of person in
Boston>”
• Rule: only send this package to someone whom you know
on a first name basis. Try to make the chain as short
as possible.
• Result: average length of chain is only six
“six degrees of separation”
• Is this really true?
– Milgram used only part of the data, actually the ones
supporting his claim
– Many packages did not end up at the Boston address
– Follow up studies all small scale
Social network analysis – introduction and some key issues
The small world phenomenon (cont.)
• “Small world project” is testing this assertion as we
speak (http://smallworld.columbia.edu), you can still
participate
• Email to <address>, otherwise same rules. Addresses
were American college professor, Indian technology
consultant, Estonian archival inspector, …
• Conclusion:
– Low completion rate (384 out of 24163 = 1.5%)
– Succesful chains more often through professional ties
– Succesful chains more often through weak ties (weak ties
mentioned about 10% more often)
– Chain size 5, 6 or 7.
Social network analysis – introduction and some key issues
The Kevin Bacon experiment – Tjaden (+/-1996)
Actors = actors ; Ties = “has
played in a movie with”
Research implications of the
small world phenomenon
-… are not yet understood very well
- it leads to diffusion that is
faster than expected (disease,
innovation, fashion)
-And … it may be good news for
sustaining cooperation …
Small world networks
-short average distance between
pairs …
- … but relatively high
“cliquishness”
Social network analysis – introduction and some key issues
The Kevin Bacon game
Can be played at:
http://www.cs.virginia.edu/oracle/
Kevin Bacon
number
Rutger Hauer (NL):
Famke Janssen (NL):
Kl.M. Brandauer (AU):
Arn. Schwarzenegger:
Franka Potente (D):
Marlene Dietrich (D):
Pascal Ulli (CH):
Bruno Ganz (CH):
2
2
2
2
2
2
3
2
[Jackie Burroughs]
[Donna Goodhand]
[Robert Redford]
[Kevin Pollak]
[Benjamin Bratt]
[Max. Schell]
[Felsenheimer, Lloyd Kaufman]
[Aidan Quinn]
Social network analysis – introduction and some key issues
How good a center is … ?
Average distance to other
actors in Internet Movie db
Rutger Hauer (NL):
Famke Janssen (NL):
Kl.M. Brandauer (AU):
Arn. Schwarzenegger:
Franka Potente (D):
Marlene Dietrich (D):
Pascal Ulli (CH):
Bruno Ganz (CH):
2.81
3.04
2.96
2.87
2.94
3.03
3.92
2.93
Kevin Bacon:
Robert de Niro:
Al Pacino:
2.94
2.77
2.87
[AS -> Charlton Heston -> MD]
Social network analysis – introduction and some key issues
Combining game theory and networks –
Axelrod (1980), Watts & Strogatz (1989)
[neural network of some wurm, power grid of electricity net, actor network]
1. Consider a given network.
2. All connected actors play the repeated Prisoner’s
Dilemma for some rounds. [indefinite vs definite]
3. After a given number of rounds, the strategies
“reproduce” in the sense that the proportion of the
more succesful strategies increases in the network,
whereas the less succesful strategies decrease or die
4. Repeat 2 and 3 until a stable state is reached.
5. Conclusion: to sustain cooperation, you need a short
average distance, and cliquishness (“small worlds”)
Social network analysis – introduction and some key issues
Collecting and analyzing network data
Social network analysis – introduction and some key issues
Social network data are tough to collect
Complete networks are huge –-> data hard and expensive
to collect through surveys if number of actors in
network is large
Gathering network data through …
– Direct observation is hardly feasible
(only possible in small scale studies)
– Available records: archives, newspapers, diaries, log
files (phone records, email records, sms, import-export
tables, etc)
– Experiments (only for small scale applications)
– Surveys  often “ego networks” only
– Other possibility: “snowball sampling” (where do you
define the boundaries?)
Social network analysis – introduction and some key issues
Ego-centered vs complete networks
1. ego-centered network analysis: network 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 partly possible with standard
software (e.g., SPSS)
• the second approach is (usually) not combined with random
sampling, often uses quantitative case study design
• statistical data analyses with specialized software (e.g.,
UCINET)
Social network analysis – introduction and some key issues
Ego-centered network data
Usually executed in a survey, often with an interviewer
• Name generator(s): Ego mentions his ties
• Tie info generator(s): Ego mentions characteristics of
his ties
• Relational data generator: Ego mentions
characteristics about the ties between his ties
Note: high burden on the respondent and complicated,
therefore interviewer necessary (but easier to
administer if done online)
Social network analysis – introduction and some key issues
Ego-centered network data
• Name generator:
E.g. “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.”
-----> try to probe five
• Tie info generator
“For these <five>, do you generally follow the advice of
this person?”
“For these <five>, how often do you talk to these persons on
matters other than personal importance?”
…
Social network analysis – introduction and some key issues
Ego-centered network data
Relational data generator:
“Now consider the relations between the contacts you
just mentioned:
Joe
Jill
Jack
John
Judy
Joe
?
?
?
?
Jill
?
?
?
Jack
?
?
John
?
Judy
-
How is the relationship between these contacts?
X=unrelated, -1=hostile, 0=neutral, 1=positive”
Social network analysis – introduction and some key issues
Network data are even tough to deal with once you have them…
[1] network as independent variable
• Suppose you have a complete network
• What is wrong with doing standard regression analysis?
– Measurement error ‘multiplies’ (extra attenuation bias)
– You have dependencies in your data that make running OLS
regressions risky
• (Note: This doesn’t play a role with ego-networks)
Social network analysis – introduction and some key issues
Network data are even tough to deal with once you have them…
[2] Network as dependent variable
• Structural elements of networks (density,
fragmentation, …) as dependent variable --> same
problems as with network as independent variable
• Network tie as dependent variable -->
huge statistical problems
check out P1-model and P2-model (and SIENA or STOCNET
software), or search for MRQAP (multiple regression
quadratic assignment procedure)
Social network analysis – introduction and some key issues
Software
• Visualization (KrackPlot, NETDraw)
• Calculation of network measures (UCINET, Pajek)
• Application of specific models (StocNET)
– Usual setup:
• you have SPSS-like (Stata, EVIEWS, Statistica, …) data
• You convert the network data to something you can import in
network software, such as in UCINET
• UCINET calculates properties (of the network and) of the
actors, and provides you with a data set that you can merge
with your original data
• Now you do “normal” statistics (t-tests, regression, etc)
(though even that may violate basic assumptions underlying
statistical testing)
Social network analysis – introduction and some key issues
Literature and readings
Social network analysis – introduction and some key issues
Literature & readings
Check out:
http://www.analytictech.com/
There is a wealth of freely available stuff on
networks online.
A (far from complete) overview is on the following
slides (taken from the site)
Social network analysis – introduction and some key issues
Literature & readings
Periodicals
Social Networks: An International Journal of Structural Analysis (1978-present). Edited by
Linton C. Freeman and Ronald L. Breiger. Many of the more technical, methodsoriented
articles about networks appear here. Available on-line through HOLLIS
beginning in 1995; see http://lib.harvard.edu/e-resources/details/s/socnetwk.html
(requires Harvard ID and PIN for access).
Connections (1977-present). Edited by William D. Richards and Thomas W. Valente.
Newsletter of the International Network for Social Network Analysis (INSNA).
[Subscription carries membership in INSNA; see http://www.sfu.ca/~insna for
information. Web version of CONNECTIONS is available six months after hardcopy
publication at the same Web address.]
Journal of Social Structure (2000-present). Edited by David Krackhardt. An electronic journal
publishing a variety of work on social networks, some of which uses display options not
available for print journals. Available free of charge at
http://www.heinz.cmu.edu/project/INSNA/joss/index1.html.
Books providing overviews:
Berkowitz, S.D. 1982. An Introduction to Structural Analysis: The Network Approach to Social
Research. Toronto: Butterworth’s.
Degenne, Alain and Michel Forsé. 1999. Introducing Social Networks. Thousand Oaks, CA:
Sage Publications.
Knoke, David. 1990. Political Networks: The Structural Perspective. New York: Cambridge
University Press.
Knoke, David and James H. Kuklinski. 1982. Network Analysis. Beverly Hills: Sage.
Monge, Peter R. and Noshir S. Contractor. 2003. Theories of Communication Networks. New
York: Oxford University Press.
Social network analysis – introduction and some key issues
Literature & readings
Collections:
Burt, Ronald S. and Michael J. Minor (eds.). 1983. Applied Network Analysis: A
Methodological Introduction. Beverly Hills: Sage. [collection of basic methods articles.]
Doreian, Patrick and Frans N. Stokman, eds. Evolution of Social Networks. Special issues of
the Journal of Mathematical Sociology, volume 21 (nos. 1-2, 1996) and volume 25 (no. 1,
2001).
Freeman, Linton C., Douglas R. White, and A. Kimball Romney (eds.). 1989. Research Methods
in Social Network Analysis. Fairfax, VA: George Mason University Press. [collection of
comparatively sophisticated methods articles from 1980 conference]
Holland, Paul W. and Samuel Leinhardt (eds.). 1979. Perspectives on Social Network Research.
New York: Academic. [collection of papers from 1975 conference.]
Leenders, Roger Th.A.J. and Shaul M. Gabbay (eds.). 1999. Corporate Social Capital and
Liability. Boston: Kluwer Academic Publishers. [collection of recent articles on social
capital in and around organizations, many of which rely on network analyses.]
Leinhardt, Samuel (ed.). 1977. Social Networks: A Developing Paradigm. New York: Academic.
[collection of relatively early articles cited by those developing the network approach.]
Lin, Nan, Karen Cook and Ronald S. Burt (eds.). 2001. Social Capital: Theory and Research.
New York: Walter de Gruyter. [collection of papers, mostly on labor markets and
communities, presented at a 1998 conference.]
Lin, Nan, Alfred Dean and Walter Ensel. 1986. Social Support, Life Events, and Depression.
New York: Academic Press.
Marsden, Peter V. and Nan Lin (eds.). 1982. Social Structure and Network Analysis. Beverly
Hills: Sage. [collection of substantively-focused articles from 1981 conference]
Mitchell, J. Clyde (ed.). 1969. Social Networks in Urban Situations. Manchester, UK:
Manchester University Press [collection of conceptual articles and applications, based on
the British social anthropological tradition]
Mizruchi, Mark S. and Michael Schwartz (eds.). 1987. Intercorporate Relations: The Structural
Analysis of Business. New York: Cambridge University Press. [collection of papers on
interlocking directorates, class cohesion, etc.]
Wasserman, Stanley, and Joseph Galaskiewicz (eds.) 1994. Advances in Social Network
Analysis: Research in the Social and Behavioral Sciences. Newbury Park, CA: Sage
Publications. [1990s stock-taking of what has been learned from the network approach in
several fields of application.]
Social network analysis – introduction and some key issues
Literature & readings
Weesie, Jeroen and Henk Flap (eds.). 1990. Social Networks Through Time. Utrecht, NL:
ISOR/University of Utrecht. [collection based on 1988 conference]
Wellman, Barry (ed.) Networks in the Global Village: Life in Contemporary Communities.
Boulder, CO: Westview Press. [collection of recent articles on personal networks and
communities.]
Wellman, Barry and S.D. Berkowitz (eds.). 1988. Social Structures: A Network Approach.
New York: Cambridge University Press. [collection of conceptual and substantive
articles which also attempts to establish links between network studies and other forms of
"structural" analysis].
Willer, David (ed.) Network Exchange Theory. Westport, CT: Praeger [collection of largely
experimental work on social exchange networks.]
Some selected book-length theoretical and substantive studies:
Burt, Ronald S. 1992. Structural Holes: The Social Structure of Competition. Cambridge, MA:
Harvard University Press.
Fischer, Claude S. 1982. To Dwell Among Friends: Personal Networks in Town and City.
Chicago: University of Chicago Press.
Friedkin, Noah E. 1998. A Structural Theory of Social Influence. New York: Cambridge
University Press.
Granovetter, Mark S. 1995. Getting a Job: A Study of Contacts and Careers. Second Edition
(first published in 1974). Chicago: University of Chicago Press.
Knoke, David, Franz Urban Pappi, Jeffrey Broadbent and Yutaka Tsujinaka. 1996. Comparing
Policy Networks: Labor Politics in the U.S., Germany, and Japan. New York:
Cambridge University Press.
Laumann, Edward O. and David Knoke. 1987. The Organizational State: Social Choice in
National Policy Domains. Madison, WI: University of Wisconsin Press.
Lin, Nan. 2001. Social Capital: A Theory of Social Structure and Action. New York:
Cambridge University Press.
Valente, Thomas W. 1995. Network Models of the Diffusion of Innovations. Cresskill, NJ:
Hampton Press.
Social network analysis – introduction and some key issues
Literature & readings
Watts, Duncan J. 1999. Small Worlds: The Dynamics of Networks between Order and
Randomness. Princeton, NJ: Princeton University Press.
Watts, Duncan J. 2003. Six Degrees: The Science of a Connected Age. New York: Norton.
Weimann, Gabriel. 1994. The Influentials: People Who Influence People. Albany, NY: State
University of New York Press.
TOPICS AND READINGS
Introduction and Overview Wasserman and Faust, chapter 1.
Scott, chapters 1-2.
Marsden, Peter V. 2000. “Social Networks.” Pp. 2727-2735 in Edgar F. Borgatta and Rhonda
J.V. Montgomery (eds.) Encyclopedia of Sociology. Second edition. New York:
MacMillan.
Marsden, Peter V. (forthcoming) “Network Analysis”, to appear in Kimberly Kempf-Leonard
(ed.) Encyclopedia of Social Measurement. San Diego, CA: Academic Press.
Egocentric Networks, Measurement, and “Social Capital”
Wasserman and Faust, chapter 2.
Scott, chapter 3.
Marsden, Peter V. 1990. "Network Data and Measurement." Annual Review of Sociology 16:
435-463.
Marsden, Peter V. (forthcoming) “Recent Developments in Network Measurement.” To appear
in Peter J. Carrington, John Scott, and Stanley Wasserman, Models and Methods in
Social Network Analysis. New York: Cambridge University Press.
Marsden, Peter V. 1987. "Core Discussion Networks of Americans." American Sociological
Review 52: 122-131.
Burt, Ronald S. 1997. “The Contingent Value of Social Capital.” Administrative Science
Quarterly 42: 339-365.
Social network analysis – introduction and some key issues
Literature & readings
Whole Networks; Introduction to Graph Theory
Wasserman and Faust, chapters 3-4.
Scott, chapter 4.
Centrality and Centralization
Wasserman and Faust, chapter 5.
Scott, chapter 5.
Freeman, Linton C. 1979. "Centrality in Social Networks: I. Conceptual Clarification." Social
Networks 1: 215-239.
Bonacich, Phillip. 1987. “Power and Centrality: A Family of Measures.” American Journal of
Sociology 92: 1170-1182.
Brass, Daniel. 1984. “Being in the Right Place: A Structural Analysis of Individual Influence in
an Organization.” Administrative Science Quarterly 29: 518-539.
Faust, Katherine. 1997. “Centrality in Affiliation Networks.” Social Networks 19: 157-191.
Subgroups in Networks, I: Cohesive Subgroups
Wasserman and Faust, chapter 7.
Scott, chapter 6
Bartholomew, David J., Fiona Steele, Irini Moustaki, and Jane I. Galbraith. 2002. The Analysis
and Interpretation of Multivariate Data for Social Scientists. London: Chapman and
Hall/CRC. Chapter 2 (“Cluster Analysis”).
Freeman, Linton C. 1992. “The Sociological Concept of ‘Group’: An Empirical Test of Two
Models.” American Journal of Sociology 98: 152-166.
Frank, Kenneth A. 1995. “Identifying Cohesive Subgroups.” Social Networks 17: 27-56.
Moore, Gwen. 1979. “The Structure of a National Elite Network.” American Sociological
Review 44: 673-692.
Krackhardt, David. 1999. "The Ties That Torture: Simmelian Tie Analysis in Organizations."
Research in the Sociology of Organizations, 16:183-210.
Social network analysis – introduction and some key issues
Literature & readings
Subgroups in Networks, II: Blockmodels/Positional Analysis
Wasserman and Faust, chapters 9, 10.
Scott, chapter 7
White, Harrison C., Scott A. Boorman and Ronald L. Breiger. 1976. “Social Structure from
Multiple Networks. I. Blockmodels of Roles and Positions.” American Journal of
Sociology 81: 730-779.
9
Borgatti, Stephen P. and Martin G. Everett. 1992. "Notions of Position in Social Network
Analysis." Pp. 1-35 in Peter V. Marsden (ed.) Sociological Methodology 1992. Oxford,
UK: Basil Blackwell, Ltd.
Breiger, Ronald L. 1981. “Structures of Economic Interdependence Among Nations.” Pp. 353380 in Peter M. Blau and Robert K. Merton (eds.) Continuities in Structural Inquiry.
Beverly Hills: Sage.
Visualizing Networks
Scott, Social Network Analysis, Chapter 8.
Freeman, Linton C. 2000. “Visualizing Social Networks.” Journal of Social Structure 1.
Electronically available at http://www.heinz.cmu.edu/project/INSNA/joss/.
Bartholomew et al., The Analysis and Interpretation of Multivariate Data for Social Scientists.
Chapters 3 (“Multidimensional Scaling”) and 4 (“Correspondence Analysis”)
Krackhardt, David, Jim Blythe and Cathleen McGrath. 1994. “KrackPlot 3.0: An Improved
Network Drawing Program.” Connections 17: 53-55.
Laumann, Edward O. and Franz U. Pappi. 1973. “New Directions in the Study of Community
Elites.” American Sociological Review 38: 212-230.
McGrath, Cathleen, Jim Blythe, and David Krackhardt. 1997. “The Effect of Spatial
Arrangement on Judgments and Errors in Interpreting Graphs.” Social Networks 19:
223-242.
Social network analysis – introduction and some key issues
Literature & readings
Analyzing and Representing “Two-Mode” Network Data
Wasserman and Faust, chapter 8
Breiger, Ronald L. 1974. "The Duality of Persons and Groups." Social Forces 53: 181-190.
Borgatti, Stephen P. and Martin G. Everett. 1997. “Network Analysis of 2-Mode Data.” Social
Networks 19: 243-269.
Bearden, James and Beth Mintz. 1987. “The Structure of Class Cohesion: The Corporate
Network and Its Dual.” Pp. 187-207 in Mark S. Mizruchi and Michael Schwartz (eds.)
Intercorporate Relations: The Structural Analysis of Business. New York: Cambridge
University Press.
Statistical Approaches to Networks: p1 and p*
Wasserman and Faust, chapters 15-16.
Anderson, Carolyn J., Stanley Wasserman and Bradley Crouch. 1999. “A p* Primer: Logit
Models for Social Networks.” Social Networks 21: 37-66.
Crouch, Bradley and Stanley Wasserman. 1997. “A Practical Guide to Fitting p* Social
Network Models Via Logistic Regression.” Connections 21: 87-101. (Download version
available at p* website, see below.)
Wasserman, Stanley, and Philippa Pattison. 1996. “Logit models and logistic regressions for
social networks: I. An introduction to Markov graphs and p*.” Psychometrika, 60: 401-426.
Skvoretz, John and Katherine Faust. 1999. “Logit Models for Affiliation Networks.” Pp. 253280 in Mark P. Becker and Michael E. Sobel (eds.) Sociological Methodology 1999.
Boston, MA: Blackwell Publishers.
Note: Additional information about p* can be found at http://kentucky.psych.uiuc.edu/pstar/
Social network analysis – introduction and some key issues
Literature & readings
Comparing Networks
Hubert, Lawrence J. and Frank B. Baker. 1978. “Evaluating the Conformity of Sociometric
Measurements.” Psychometrika 43: 31-41.
Baker, Frank B. And Lawrence J. Hubert. 1981. “The Analysis of Social Interaction Data: A
Nonparametric Technique.” Sociological Methods and Research 9: 339-361.
Krackhardt, David. 1987. “QAP Partialling as a Test of Spuriousness.” Social Networks 9:
171-186.
Faust, Katherine and John Skvoretz. 2002. “Comparing Networks Across Time and Space, Size
and Species.” Pp. 267-299 in Ross M. Stolzenberg (ed.) Sociological Methodology
2002. Boston, MA: Blackwell Publishing.
Cognitive Social Structure Data
Krackhardt, David. 1987. “Cognitive Social Structures.” Social Networks 9: 109-134.
Kumbasar, Ece, A. Kimball Romney and William H. Batchelder. 1994. “Systematic Biases in
Social Perception.” American Journal of Sociology 100: 477-505.
Krackhardt, David 1990. “Assessing the Political Landscape: Structure, Cognition, and Power in
Organizations.” Administrative Science Quarterly 35: 342-369.
Models for Studying Network Effects and Diffusion
Marsden, Peter V. and Noah E. Friedkin. 1994. "Network Studies of Social Influence." Pp. 3-25
in Wasserman and Galaskiewicz (eds.) Advances in Social Network Analysis.
Ibarra, Herminia and Steven B. Andrews. 1993. “Power, Social Influence, and Sense-Making:
Effects of Network Centrality and Proximity on Employee Perceptions.” Administrative
Science Quarterly 38: 277-304.
Hedström, Peter, Rickard Sandell and Charlotta Stern. 2000. “Mesolevel Networks and the
Diffusion of Social Movements: The Case of the Swedish Social Democratic Party.”
American Journal of Sociology 106: 145-172.
Strang, David and Nancy Brandon Tuma. 1993. “Spatial and Temporal Heterogeneity in
Diffusion.” American Journal of Sociology 99: 614-639.
Morris, Martina. 1994. “Epidemiology and Social Networks: Modeling Structured Diffusion.”
Pp. 26-52 in Wasserman and Galaskiewicz (eds.) Advances in Social Network Analysis.
Social network analysis – introduction and some key issues
Literature & readings
Longitudinal Network Analysis
11
Snijders, Tom A.B. 1996. “Stochastic Actor-Oriented Models for Network Change.” Journal of
Mathematical Sociology 21: 149-172.
Van de Bunt, Gerhard G., Marijte A.J. van Duijn and Tom A.B. Snijders. 1999. “Friendship
Networks Through Time: An Actor-Oriented Statistical Network Model.”
Computational and Mathematical Organization Theory 5: 167-192.
Network Sampling
Scott, chapter 3 (end)
Granovetter, Mark. 1976. “Network Sampling: Some First Steps.” American Journal of
Sociology 81: 1287-1303.
Frank, Ove. 1978. “Sampling and Estimation in Large Social Networks.” Social Networks 1:
91-101.
Klovdahl, Alden S., Z. Dhofier, G. Oddy, J. O’Hara, S. Stoutjesdijk, and A. Whish. 1977.
“Social Networks in an Urban Area: First Canberra Study.” Australian and New Zealand
Journal of Sociology 13: 169-172.
Social network analysis – introduction and some key issues
Network measures
And
Dealing with
your data
Social network analysis – introduction and some key issues
General setup of a scientific paper
• Problem formulation – Theory – Observation
EXAMPLE
• Problem: Which firms tend to produce more innovations?
• Theory: This has to do with at least three factors
– Capability of personnel (a firm characteristic)
– Competiveness of the market (a context characteristic)
– The way in which a firm is connected to other firms (a
network characteristic)
• Observation: …
Social network analysis – introduction and some key issues
Your data look like this …
Capa
bility
Competetive
Network
property
Innovations
Firm 1
10
34
?
40
Firm 2
13
50
?
12
Firm 3
26
20
?
33
…
Firm 523
23
88
?
22
So we want to predict whether a firm is producting innovations from
the other columns (capability, competitiveness, some network
property) in the data.
How do we do this?
Social network analysis – introduction and some key issues
IN SPSS WE HAVE:
SPSS to
UCINET
to SPSS
WE TAKE:
uid n1
[1]
uid x1
x2 …
n1
n2 …
n31
1
0
23
9
2
…
3
2
0
22
4
9
…
1
3
1
28
1
1
…
4
…
…
…
…
…
…
…
31
0
25
2
1
…
9
TO GET: [3]
[2]
n2
…
n31
uid Measure
1
0.12
2
0.34
3
0.25
…
1
9
2
…
3
2
4
9
…
1
3
1
1
…
4
…
…
…
…
…
…
1
…
9
31 0.94
31 2
through
Ucinet
… WE THEN MERGE [3] TO [1] ON <uid>,
AND RUN AN ANALYSIS IN SPSS ON THE MERGED FILES
Social network analysis – introduction and some key issues
Network measures (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:
NOTE2:
NOTE3:
NOTE4:
this is a locally defined measure, that is, a measure that is defined for each actor separately
this gives rise to several global network measures, such as (in/out)degree variance
if your network is not directed, indegree and outdegree are the same and called degree
these measures can be constructed in SPSS; no need for special purpose software. Try this yourself!
Social network analysis – introduction and some key issues
Network measures (2):
number of ties of a certain quality
1
2
3
4
5
=
=
=
=
=
do not even know this firm
have heard of this firm, have never dealt with it
know this firm, have dealt with it once or twice
have dealt with this firm regularly
this firm is a strategic partner
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:
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)
This kind of recoding can be easily done in any general
purpose statistics program, such as SPSS
Social network analysis – introduction and some key issues
Network measures (3): global degree
Degree centrality as a global network concept
(“the degree to which there are central actors”)
For each network,
outdegree centrality = the variance of the outdegrees
The more the outdegrees ‘are the same’, the less
central actors are.
(The same goes for indegree centrality)
NOTE: there are many more centrality measures
Social network analysis – introduction and some key issues
Network measures (4): the most common global
network property
Density:
For each network: the number of (valued) relations,
relative to the maximum possible number of (valued)
relations.
=
i,j
rij
/ N (N-1) R
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
Social network analysis – introduction and some key issues
Network measures (5): 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
Or sometimes researchers use ‘generalized distance’:
– E.g.: the cost of a path is the sum of all values on the edges of a path. The
distance is the cheapest cost.
– Or: the value of a path is the value of its weakest link. The distance is the path
with the highest value.
For every actor i, average distance =
j
Dij / N
NOTE: THIS IS NOT EASY TO DO ANYMORE IN SPSS!
Social network analysis – introduction and some key issues
Network measures (6): betweenness
Centrality and power again: betweenness
= the percentage of times an actor is in between other
actors
Betweenness for actor i =
1. For all pairs (j,k) consider all possible geodesics from j to k.
2. Calculate the proportion of times that actor i is on a geodesic
from j to k.
3. Betweenness is the sum of these proportions over all pairs (j,k).
 This measure varies between 0 and (N-1)(N-2)/2
(the number of ways in which a sample of 2 can be taken from the N1 other actors). It is therefore usually normalized, by dividing it
by (N-1)(N-2)/2. Then it varies between 0 and 1, and we can compare
it also across networks.
NOTE: THIS AGAIN IS NOT EASY TO DO ANYMORE IN SPSS. FOR THIS YOU
HAVE TO USE OTHER SOFTWARE, SUCH AS UCINET
Social network analysis – introduction and some key issues
Network measures (7): information centrality
(it’s betweenness but different)
Centrality and power again: information centrality
= the percentage of times an actor is in between other
actors
Betweenness for actor i =
1. For all pairs (j,k) consider all possible paths from j to k.
2. To each path, we give a weight that is inversely proportional to
its length (“a shorter path is more likely”).
3. We sum the weights for each path that has i on it (A), and for each
path that does not have i on it (B).
4. Information centrality for actor i with respect to (j,k) equals A /
(A+B)
5. Information centrality for actor i is then the sum of these
proportions over all values (j,k) (again: usually normalized)
NOTE: THIS AGAIN IS NOT EASY TO DO ANYMORE IN SPSS. FOR THIS YOU
HAVE TO USE OTHER SOFTWARE, SUCH AS UCINET
Social network analysis – introduction and some key issues
Other network measures
we could have used …
• Transitivity = the degree to which the statement
“If i is connected to j, and j is connected to k, then
i is connected to k”, is true
• N-cliques =
An N-clique of an undirected graph is a maximal
subgraph in which every pair of nodes is connected by
a path of length N or less.
• … and many more (part of it in class next 2 times)
Social network analysis – introduction and some key issues
IN SPSS WE HAVE:
SPSS to
UCINET
to SPSS
WE TAKE:
uid n1
[1]
uid x1
x2 …
n1
n2 …
n31
1
0
23
9
2
…
3
2
0
22
4
9
…
1
3
1
28
1
1
…
4
…
…
…
…
…
…
…
31
0
25
2
1
…
9
TO GET: [3]
[2]
n2
…
n31
uid Measure
1
0.12
2
0.34
3
0.25
…
1
9
2
…
3
2
4
9
…
1
3
1
1
…
4
…
…
…
…
…
…
1
…
9
31 0.94
31 2
through
Ucinet
… WE THEN MERGE [3] TO [1] ON <uid>,
AND RUN AN ANALYSIS IN SPSS ON THE MERGED FILES
Social network analysis – introduction and some key issues
A brief view on Ucinet
Importing data using DL-files
----------------------dl n=31
Labels:
AB…Z
data:
01342…
10435…
…
32154…
-----------------------
Calculating network properties
using data in Ucinet-format
Two files are created:
<name>.##h
<name>.##d
Social network analysis – introduction and some key issues
Ucinet basics
•
•
•
•
•
Changing the basic path
Reading DL-files
Calculating network measures
Transforming the data matrix
(viewing the network)
NOTE: some measures can be calculated on binary
network data only! When confronted with data that are
not binary, Ucinet often makes the data binary for
that particular calculation! (try:
Network>Betweenness>Nodes)
• Merging the data into SPSS
Social network analysis – introduction and some key issues
Some final issues
Social network analysis – introduction and some key issues
General issues in social network analysis
•
Think carefully about what defines an actor (often simple) and what defines a
tie (often complicated)
•
Always think carefully about which property of the network it is, that drives
the effect (closeness, betweenness, density, something else)
•
Think beforehand about how to tackle the data, and build in proxies in the
data collection. Using (only) directly measured network data is risky.
•
When it comes to statistics, know that network data have their own typical
problems that sometimes cannot (yet) be solved with standard SPSS-like
packages.
•
There is still something to gain here for researchers: network research is
still in its infancy.
•
We have just created a “weak tie”. If you have any questions related to
social networks, ask! ([email protected])
•
General info on networks? Try www.analytictech.com/networks or put yourself
on the social network (socnet) mailinglist www.insna.org .
Social network analysis – introduction and some key issues