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Social network analysis

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Title: Social network analysis


1
Social network analysis
  • Chris Snijders
  • Dept of Technology Management
  • Cap. group Technology Policy
  • Eindhoven University of Technology
  • Eindhoven, The Netherlands
  • c.c.p.snijders_at_tm.tue.nl
  • note material partly collected online!

2
Program
  • 900 1230 and 1330 1700
  • 0900 0915 A brief inventory
  • 0915 1030 Introduction to social network
    analysis and
  • social capital theory,
  • typical research questions
  • 1030 1045
  • 1045 1230 Some classic social network
    studies
  • 1230 1330
  • 1330 1430 Network concepts and network
    measurements
  • 1430 1515 Dealing with network analysis
  • 1515 1530
  • 1530 1615 A brief look on network analysis
    software
  • 1615 1700 Leftovers / assignment
  • Note slides will be available online later

3


Brief introduction to social network analysis
4
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
5
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
6
(No Transcript)
7
Example network (source Borgatti)
8
Example network a food chain
9
Why do networks matter?
10
Why do networks matter?
11
practical classics
12
The network perspective
Two firms in the same market. Which firm performs
better (say, is more innovative) A or B?
  • This depends on
  • Cost effectiveness
  • Organizational structure
  • Corporate culture
  • Flexibility
  • Supply chain management

13
The network perspective
Two firms in the same market. Which firm performs
better (say, more innovative) A or B?
Note Networks are one specific way of dealing
with market imperfection
AND POSITION IN THE NETWORK OF FIRMS
14
Origins of social network research
  • Main development in social sciences in the 30s.
  • 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)
  • 50s conflicts in groups (Barnes, Bott, White)
  • And mathematics has been working on points and
    lines (graph theory) for a long time.

15
Increasing popularity
16
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?

17
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

18
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 datainside
    a consulting firm. I received many useful bits of
    informationincluding 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

19
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

20
Some key social network books
  • 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

21
Social network software
  • UCINet Many things on network analysis
  • Lin Freeman, Steve Borgatti, Martin Everett
  • MultiNet Whole Network Analysis
  • Nodal Characteristics
  • Structure Ron Burt No longer maintained
  • PStar Dyadic Analysis Stan Wasserman
  • Krackplot Network Visualization (Obsolete)
  • David Krackhardt, Jim Blythe
  • Pajek Network Visualization Supersedes
    Krackplot
  • StocNet Tom Snijders - collected programs for,
    e.g., analysis of dynamic networks

22
Kinds of data collection through SNA history
  • Small Group Sociometry1930s (Moreno,
    Bonacich, Cook)
  • Finding People Who Enjoy Working Together
  • Evolved into Exchange Theory, Small Group Studies
  • Ethnographic Studies, 1950s (Mitchell, Barnes)
  • Does Modernization Disconnection?
  • Survey Research Personal Networks, 1970s
  • Community, Support Social Capital, Guanxi
  • Mathematics Simulation, 1970s (Freeman,
    White)
  • Formalist / Methods Substantive Analysis
  • Survey Archival Research, Whole Nets, 1970s
  • Organizational, Inter-Organizational,
    Inter-National Analyses
  • Political Structures, 1970s (Tilly,
    Wallerstein)
  • Social Movements, Mobilization (anti Alienation)
  • World Systems (asymmetric structure
    Globalization)
  • Computer Networks as Social Networks, late 1990s
    (Sack)
  • Automated Data Collection

23
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

24
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

25
Example relations among organizations
  • Firms 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
  • Firm members as actors
  • Has a personal friend in board of
  • Has a personnel flow to
  • Have an interlocking board

26
Example network Collaboration between
disciplines (source Borgatti)
27
Example network terrorists (source Borgatti)
28
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 Burts Structural Holes
    book)
  • Human capital beats social capital (the real
    individualist)
  • ? at least, consider how social capital can be of
    influence

29


Some typical research questions in social network
analysis
30
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
    doesnt
  • (firm A has a higher outdegree)

31
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?

32
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

33
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!
  • Dont 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.

34
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

35
Typical social network research questions
  • How is property X of an actor related to his or
    her social network properties?
  • X actor type network char.
  • job success individual structural holes
  • well-being individual outdegree
  • longeveity individual freq. of contacts
  • innovativeness firm closure

36


Network concepts
37
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
38
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

1
4
8
2
2
5
1
39
Network representations graph and matrix
  • A 1-mode, non-valued, directed network

A 1-mode, non-valued, undirected network
A
B
9
1
4
3
C
D
40
Kinds of network data
AND another dimension directed relations or
undirected
41
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?

42
Some network concepts
Walk gets from A to X A-C-A-D-F-X Trail Walk,
but without repeating lines A-D-E-F-D-B-X Path W
alk, but without repeating nodes A-D-E-F-X
Distance between A and X Length of shortest path
(geodesic distance) Connected graph For any
couple of nodes there exists a path from one to
the other
43
More network concepts
X
Cutpoints Nodes which, if deleted, would
disconnect the network. For instance, node
D. Bridges Ties which, if deleted, would
disconnect the network. For instance, the tie
between A and D.
E
C
F
D
A
B
44
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
  • 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

45
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?)

46


About network literature
47
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
48
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.

49
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

50
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

51


Research classic Granovetters (1973) Strength
of weak ties as a precursor to Burts structural
holes
52
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
  • Granovetters 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

53
Mark GranovetterThe 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 Granovetters paper

54
Mark Granovetterother 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

55
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. Here A has more than B
56


Research classic Burts (1988) Structural
holes as a response to Colemans closure
argument
57
Ron BurtStructural holes versus network closure
as social capital
  • Burts 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
  • He subsequently compares people with
  • dense networks with those with
  • networks rich in structural holes

University of Chicago graduate school of business
58
Social organization
Structural holes create value
A
B
1
7
3
2
James
Robert
4
5
6
  • Robert will do better than James, because of
  • informational benefits
  • tertius gaudens (entrepreneur)

C
59
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

60
Structural holes vs network closure
  • Empirical evidence on
  • Dependent variable early promotion
  • large bonus
  • outstanding evaluation
  • all seem to favor Burts structural holes
  • Burt on Coleman
  • Colemans 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.

61
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 ?

62


Research classic The small world phenomenon
and theoretical research into social
networks Or one typical kind of network
structure
63
The small world phenomenon Milgram (1967)
  • Milgram sent packages to a couple hundred people
    in Nebraska and Kansas.
  • Aim was get this package to 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

64
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 , 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.

65
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

66
The Kevin Bacon game
  • Can be played at
  • http//www.cs.virginia.edu/oracle/
  • Kevin Bacon
  • number
  • Rutger Hauer (NL) 2 Jackie Burroughs
  • Famke Janssen (NL) 2 Donna Goodhand
  • Kl.M. Brandauer (AU) 2 Robert Redford
  • Arn. Schwarzenegger 2 Kevin Pollak
  • Franka Potente (D) 2 Benjamin Bratt
  • Marlene Dietrich (D) 2 Max. Schell
  • Pascal Ulli (CH) 3 Felsenheimer, Lloyd
    Kaufman
  • Bruno Ganz (CH) 2 Aidan Quinn

67
How good a center is ?
  • Average distance to other
  • actors in Internet Movie db
  • Rutger Hauer (NL) 2.81
  • Famke Janssen (NL) 3.04
  • Kl.M. Brandauer (AU) 2.96
  • Arn. Schwarzenegger 2.87
  • Franka Potente (D) 2.94
  • Marlene Dietrich (D) 3.03
  • Pascal Ulli (CH) 3.92
  • Bruno Ganz (CH) 2.93
  • Kevin Bacon 2.94
  • Robert de Niro 2.77
  • Al Pacino 2.87 AS - Charlton Heston - MD

68
Combining game theory and networks Axelrod
(1980), Watts Strogatz (1989) neural network
of some wurm, power grid of electricity net,
actor network
  • Consider a given network.
  • All connected actors play the repeated Prisoners
    Dilemma for some rounds. indefinite vs definite
  • 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
  • Repeat 2 and 3 until a stable state is reached.
  • Conclusion to sustain cooperation, you need a
    short average distance, and cliquishness (small
    worlds)

69


Collecting and analyzing network data
70
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?)

71
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)

72
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)

73
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 , do you generally follow the
    advice of this person?
  • For these , how often do you talk to
    these persons on matters other than personal
    importance?

74
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?
  • Xunrelated, -1hostile, 0neutral, 1positive

75
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 doesnt play a role with ego-networks)

76
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)

77
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)

78


Literature and readings
79
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)

80
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-re
    sources/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

81
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

82
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.

83
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.

84
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

85
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. 353-
  • 380 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.e
    du/project/INSNA/joss/.
  • Bartholomew et al., The Analysis and
    Interpretation of Multivariate Data for Social
    Scientists.

86
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.

87
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

88
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.
    OHara, 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.

89


Network measures And Dealing with your data
90
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

91
Your data look like this
  • Capa Compe- Network Innova-
    bility tetive property tions
  • 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?

92
SPSS to UCINET to SPSS
IN SPSS WE HAVE
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 uid Measure 1 0.12 2 0.34 3
0.25 31 0.94
WE TAKE 2 uid n1 n2
n31 1 9 2 3 2 4 9
1 3 1 1 4
31 2 1 9
through Ucinet
WE THEN MERGE 3 TO 1 ON , AND RUN AN
ANALYSIS IN SPSS ON THE MERGED FILES
93
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 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!

94
Network measures (2) number of ties of a
certain quality
  • 1 do not even know this firm
  • 2 have heard of this firm, have never dealt
    with it
  • 3 know this firm, have dealt with it once or
    twice
  • 4 have dealt with this firm regularly
  • 5 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

95
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

96
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

97
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!

98
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 N-1 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

99
Network measures (7) information centrality
(its 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 / (AB)
  • 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

100
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)

101
SPSS to UCINET to SPSS
IN SPSS WE HAVE
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 uid Measure 1 0.12 2 0.34 3
0.25 31 0.94
WE TAKE 2 uid n1 n2
n31 1 9 2 3 2 4 9
1 3 1 1 4
31 2 1 9
through Ucinet
WE THEN MERGE 3 TO 1 ON , AND RUN AN
ANALYSIS IN SPSS ON THE MERGED FILES
102
A brief view on Ucinet
Importing data using DL-files
----------------------- dl n31 Labels A B
Z data 0 1 3 4 2 1 0 4 3 5 3 2 1 5 4
----------------------- Calculating network
properties using data in Ucinet-format Two files
are created .h .d
103
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
    NetworkBetweennessNodes)
  • Merging the data into SPSS

104


Some final issues
105
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!
    (c.c.p.snijders_at_tm.tue.nl)
  • General info on networks? Try www.analytictech.com
    /networks or put yourself on the social network
    (socnet) mailinglist www.insna.org .
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