1. Social network analysis
Chris Snijders
Dept of Technology Management
Cap. group Technology & Policy
Eindhoven University of Technology
Eindhoven, The Netherlands
[note: material partly collected online!]
Social network analysis – introduction and some key issues

2. 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

3. Brief introduction to social network analysis
Social network analysis – introduction and some key issues

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
Social network analysis – introduction and some key issues

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
Social network analysis – introduction and some key issues

6. Social network analysis – introduction and some key issues

7. Example network (source: Borgatti)
Social network analysis – introduction and some key issues

8. Example network: a food “chain”
Social network analysis – introduction and some key issues

9. Why do networks matter?
Social network analysis – introduction and some key issues

10. Why do networks matter?
Social network analysis – introduction and some key issues

11. “practical classics”
Social network analysis – introduction and some key issues

12. 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

13. The network perspective
Two firms in the same market.
Which firm performs better (say, more innovative): A or B? A B
Note
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

14. 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

15. Increasing popularity
Social network analysis – introduction and some key issues

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?
Social network analysis – introduction and some key issues

17. The International Network of Social Network Analysis (INSNA)
Founded by Barry Wellman in
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:

18. The socnet-mailing list
*****  To join INSNA, visit ***** 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

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
Social network analysis – introduction and some key issues

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
P*Star – 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 “Sociometry”1930s > (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
Social network analysis – introduction and some key issues

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
Social network analysis – introduction and some key issues

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
Social network analysis – introduction and some key issues

26. Example network: Collaboration between disciplines (source: Borgatti)
Social network analysis – introduction and some key issues

27. Example network: terrorists (source: Borgatti)
Social network analysis – introduction and some key issues

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 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

29. Some typical research questions in social network analysis
Social network analysis – introduction and some key issues

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 doesn’t
(firm A has a higher “outdegree”)
Social network analysis – introduction and some key issues

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
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

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  
Social network analysis – introduction and some key issues

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!
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

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
Social network analysis – introduction and some key issues

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
… … …
Social network analysis – introduction and some key issues

36. Network concepts
Social network analysis – introduction and some key issues

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
Social network analysis – introduction and some key issues

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
Social network analysis – introduction and some key issues

39. Network representations: graph and matrix
A 1-mode, non-valued, directed network A B C D - 1 A B C D
A 1-mode, non-valued, undirected network A B C D - 9 4 1 3 A B 9 1 4 3 C D
Social network analysis – introduction and some key issues

40. AND another dimension: directed relations or undirected
Kinds of network data
AND another dimension: directed relations or undirected
Social network analysis – introduction and some key issues

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?
Social network analysis – introduction and some key issues

42. Some network concepts Walk gets from A to X: A-C-A-D-F-X TrailB F X
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
Walk, 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
Social network analysis – introduction and some key issues

43. More network concepts CutpointsX
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
Social network analysis – introduction and some key issues

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 A B C D - 1
Social network analysis – introduction and some key issues

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?)
Social network analysis – introduction and some key issues

46. About network literature
Social network analysis – introduction and some key issues

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
Social network analysis – introduction and some key issues

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.
Social network analysis – introduction and some key issues

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
Social network analysis – introduction and some key issues

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
- circles
- use of msn etc
Social network analysis – introduction and some key issues

51. “Strength of weak ties” as a precursor to Burt’s structural holes
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

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
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

53. 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

54. 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

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 A B
Social network analysis – introduction and some key issues

56. “Structural holes” as a response to Coleman’s closure argument
Research classic:
Burt’s (1988)
“Structural holes” as a response to Coleman’s closure argument
Social network analysis – introduction and some key issues

57. 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]
He subsequently compares people with
dense networks with those with
networks rich in “structural holes”
University of Chicago graduate school of business
Social network analysis – introduction and some key issues

58. Social organization A B James Robert C “Structural holes create value”1 B 7 3 2
James
Robert 4 5 6
Robert will do better than James, because of:
informational benefits
“tertius gaudens” (entrepreneur) C
Social network analysis – introduction and some key issues

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
Social network analysis – introduction and some key issues

60. 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

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 …?
Social network analysis – introduction and some key issues

62. Or: one typical kind of network structure
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

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 <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

64. The small world phenomenon (cont.)
“Small world project” is testing this assertion as we speak ( you can still participate
to <address>, otherwise same rules. Addresses were American college professor, Indian technology consultant, Estonian archival inspector, …
Conclusion:
Low completion rate (384 out of = 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

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”
Social network analysis – introduction and some key issues

66. The Kevin Bacon game Can be played at:
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]
Social network analysis – introduction and some key issues

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):
Bruno Ganz (CH):
Kevin Bacon:
Robert de Niro:
Al Pacino: [AS -> Charlton Heston -> MD]
Social network analysis – introduction and some key issues

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 Prisoner’s 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”)
Social network analysis – introduction and some key issues

69. Collecting and analyzing network data
Social network analysis – introduction and some key issues

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, 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

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)
Social network analysis – introduction and some key issues

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)
Social network analysis – introduction and some key issues

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 <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

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?
X=unrelated, -1=hostile, 0=neutral, 1=positive”
Social network analysis – introduction and some key issues

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 doesn’t play a role with ego-networks)
Social network analysis – introduction and some key issues

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)
Social network analysis – introduction and some key issues

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)
Social network analysis – introduction and some key issues

78. Literature and readings
Social network analysis – introduction and some key issues

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)
Social network analysis – introduction and some key issues

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
(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 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
Books providing overviews:
Berkowitz, S.D An Introduction to Structural Analysis: The Network Approach to Social
Research. Toronto: Butterworth’s.
Degenne, Alain and Michel Forsé Introducing Social Networks. Thousand Oaks, CA:
Sage Publications.
Knoke, David Political Networks: The Structural Perspective. New York: Cambridge
University Press.
Knoke, David and James H. Kuklinski Network Analysis. Beverly Hills: Sage.
Monge, Peter R. and Noshir S. Contractor Theories of Communication Networks. New
York: Oxford University Press.
Social network analysis – introduction and some key issues

81. Literature & readings Collections:
Burt, Ronald S. and Michael J. Minor (eds.) 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.) 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.) Perspectives on Social Network Research.
New York: Academic. [collection of papers from 1975 conference.]
Leenders, Roger Th.A.J. and Shaul M. Gabbay (eds.) 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.) 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.) 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 Social Support, Life Events, and Depression.
New York: Academic Press.
Marsden, Peter V. and Nan Lin (eds.) Social Structure and Network Analysis. Beverly
Hills: Sage. [collection of substantively-focused articles from 1981 conference]
Mitchell, J. Clyde (ed.) 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.) 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.) 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

82. Literature & readings
Weesie, Jeroen and Henk Flap (eds.) 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.) 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 Structural Holes: The Social Structure of Competition. Cambridge, MA:
Harvard University Press.
Fischer, Claude S To Dwell Among Friends: Personal Networks in Town and City.
Chicago: University of Chicago Press.
Friedkin, Noah E A Structural Theory of Social Influence. New York: Cambridge
University Press.
Granovetter, Mark S 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 Comparing
Policy Networks: Labor Politics in the U.S., Germany, and Japan. New York:
Cambridge University Press.
Laumann, Edward O. and David Knoke The Organizational State: Social Choice in
National Policy Domains. Madison, WI: University of Wisconsin Press.
Lin, Nan Social Capital: A Theory of Social Structure and Action. New York:
Valente, Thomas W Network Models of the Diffusion of Innovations. Cresskill, NJ:
Hampton Press.
Social network analysis – introduction and some key issues

83. Literature & readings
Watts, Duncan J Small Worlds: The Dynamics of Networks between Order and
Randomness. Princeton, NJ: Princeton University Press.
Watts, Duncan J Six Degrees: The Science of a Connected Age. New York: Norton.
Weimann, Gabriel 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 “Social Networks.” Pp 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 "Network Data and Measurement." Annual Review of Sociology 16:
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 "Core Discussion Networks of Americans." American Sociological
Review 52:
Burt, Ronald S “The Contingent Value of Social Capital.” Administrative Science
Quarterly 42:
Social network analysis – introduction and some key issues

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 "Centrality in Social Networks: I. Conceptual Clarification." Social
Networks 1:
Bonacich, Phillip “Power and Centrality: A Family of Measures.” American Journal of
Sociology 92:
Brass, Daniel “Being in the Right Place: A Structural Analysis of Individual Influence in
an Organization.” Administrative Science Quarterly 29:
Faust, Katherine “Centrality in Affiliation Networks.” Social Networks 19:
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 The Analysis
and Interpretation of Multivariate Data for Social Scientists. London: Chapman and
Hall/CRC. Chapter 2 (“Cluster Analysis”).
Freeman, Linton C “The Sociological Concept of ‘Group’: An Empirical Test of Two
Models.” American Journal of Sociology 98:
Frank, Kenneth A “Identifying Cohesive Subgroups.” Social Networks 17:
Moore, Gwen “The Structure of a National Elite Network.” American Sociological
Review 44:
Krackhardt, David "The Ties That Torture: Simmelian Tie Analysis in Organizations."
Research in the Sociology of Organizations, 16:
Social network analysis – introduction and some key issues

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 “Social Structure from
Multiple Networks. I. Blockmodels of Roles and Positions.” American Journal of
Sociology 81: 9
Borgatti, Stephen P. and Martin G. Everett "Notions of Position in Social Network
Analysis." Pp in Peter V. Marsden (ed.) Sociological Methodology Oxford,
UK: Basil Blackwell, Ltd.
Breiger, Ronald L “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 “Visualizing Social Networks.” Journal of Social Structure 1.
Electronically available at
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 “KrackPlot 3.0: An Improved
Network Drawing Program.” Connections 17:
Laumann, Edward O. and Franz U. Pappi “New Directions in the Study of Community
Elites.” American Sociological Review 38:
McGrath, Cathleen, Jim Blythe, and David Krackhardt “The Effect of Spatial
Arrangement on Judgments and Errors in Interpreting Graphs.” Social Networks 19:
Social network analysis – introduction and some key issues

86. Literature & readings
Analyzing and Representing “Two-Mode” Network Data
Wasserman and Faust, chapter 8
Breiger, Ronald L "The Duality of Persons and Groups." Social Forces 53:
Borgatti, Stephen P. and Martin G. Everett “Network Analysis of 2-Mode Data.” Social
Networks 19:
Bearden, James and Beth Mintz “The Structure of Class Cohesion: The Corporate
Network and Its Dual.” Pp 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
Anderson, Carolyn J., Stanley Wasserman and Bradley Crouch “A p* Primer: Logit
Models for Social Networks.” Social Networks 21:
Crouch, Bradley and Stanley Wasserman “A Practical Guide to Fitting p* Social
Network Models Via Logistic Regression.” Connections 21: (Download version
available at p* website, see below.)
Wasserman, Stanley, and Philippa Pattison “Logit models and logistic regressions for
social networks: I. An introduction to Markov graphs and p*.” Psychometrika, 60:
Skvoretz, John and Katherine Faust “Logit Models for Affiliation Networks.” Pp. 253-
280 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
Social network analysis – introduction and some key issues

87. Literature & readings Comparing Networks
Hubert, Lawrence J. and Frank B. Baker “Evaluating the Conformity of Sociometric
Measurements.” Psychometrika 43:
Baker, Frank B. And Lawrence J. Hubert “The Analysis of Social Interaction Data: A
Nonparametric Technique.” Sociological Methods and Research 9:
Krackhardt, David “QAP Partialling as a Test of Spuriousness.” Social Networks 9:
Faust, Katherine and John Skvoretz “Comparing Networks Across Time and Space, Size
and Species.” Pp in Ross M. Stolzenberg (ed.) Sociological Methodology
2002. Boston, MA: Blackwell Publishing.
Cognitive Social Structure Data
Krackhardt, David “Cognitive Social Structures.” Social Networks 9:
Kumbasar, Ece, A. Kimball Romney and William H. Batchelder “Systematic Biases in
Social Perception.” American Journal of Sociology 100:
Krackhardt, David “Assessing the Political Landscape: Structure, Cognition, and Power in
Organizations.” Administrative Science Quarterly 35:
Models for Studying Network Effects and Diffusion
Marsden, Peter V. and Noah E. Friedkin "Network Studies of Social Influence." Pp. 3-25
in Wasserman and Galaskiewicz (eds.) Advances in Social Network Analysis.
Ibarra, Herminia and Steven B. Andrews “Power, Social Influence, and Sense-Making:
Effects of Network Centrality and Proximity on Employee Perceptions.” Administrative
Science Quarterly 38:
Hedström, Peter, Rickard Sandell and Charlotta Stern “Mesolevel Networks and the
Diffusion of Social Movements: The Case of the Swedish Social Democratic Party.”
American Journal of Sociology 106:
Strang, David and Nancy Brandon Tuma “Spatial and Temporal Heterogeneity in
Diffusion.” American Journal of Sociology 99:
Morris, Martina “Epidemiology and Social Networks: Modeling Structured Diffusion.”
Pp in Wasserman and Galaskiewicz (eds.) Advances in Social Network Analysis.
Social network analysis – introduction and some key issues

88. Literature & readings
Longitudinal Network Analysis 11
Snijders, Tom A.B “Stochastic Actor-Oriented Models for Network Change.” Journal of
Mathematical Sociology 21:
Van de Bunt, Gerhard G., Marijte A.J. van Duijn and Tom A.B. Snijders “Friendship
Networks Through Time: An Actor-Oriented Statistical Network Model.”
Computational and Mathematical Organization Theory 5:
Network Sampling
Scott, chapter 3 (end)
Granovetter, Mark “Network Sampling: Some First Steps.” American Journal of
Sociology 81:
Frank, Ove “Sampling and Estimation in Large Social Networks.” Social Networks 1:
Klovdahl, Alden S., Z. Dhofier, G. Oddy, J. O’Hara, S. Stoutjesdijk, and A. Whish
“Social Networks in an Urban Area: First Canberra Study.” Australian and New Zealand
Journal of Sociology 13:
Social network analysis – introduction and some key issues

89. Network measures And Dealing with your data
Social network analysis – introduction and some key issues

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: …
Social network analysis – introduction and some key issues

91. Your data look like this …
Capa Compe- Network Innova- bility tetive property tions
Firm ? 40
Firm ? 12
Firm ? 33 …
Firm ? 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

92. SPSS to UCINET to SPSS 1 0 23 9 2 … 3 2 0 22 4 9 … 1 3 1 28 1 1 … 4
IN SPSS WE HAVE: [1]
uid x x2 … n1 n2 … n31
… 3
… 1
… 4
… … … … … … …
… 9
SPSS to UCINET to SPSS
WE TAKE: [2]
uid n1 n2 … n31
… 3
… 1
… 4
… … … … …
… 9
TO GET: [3]
uid Measure
… …
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

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!
Social network analysis – introduction and some key issues

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
Social network analysis – introduction and some key issues

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
Social network analysis – introduction and some key issues

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
Social network analysis – introduction and some key issues

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!
Social network analysis – introduction and some key issues

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
Social network analysis – introduction and some key issues

99. 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

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)
Social network analysis – introduction and some key issues

101. SPSS to UCINET to SPSS 1 0 23 9 2 … 3 2 0 22 4 9 … 1 3 1 28 1 1 … 4
IN SPSS WE HAVE: [1]
uid x x2 … n1 n2 … n31
… 3
… 1
… 4
… … … … … … …
… 9
SPSS to UCINET to SPSS
WE TAKE: [2]
uid n1 n2 … n31
… 3
… 1
… 4
… … … … …
… 9
TO GET: [3]
uid Measure
… …
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

102. A brief view on Ucinet Importing data using DL-files
dl n=31
Labels:
A B … Z
data: … … … …
Calculating network properties using data in Ucinet-format
Two files are created:
<name>.##h
<name>.##d
Social network analysis – introduction and some key issues

103. Changing the basic path Reading DL-files Calculating network measures
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

104. Some final issues
Social network analysis – introduction and some key 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!
General info on networks? Try or put yourself on the social network (socnet) mailinglist .
Social network analysis – introduction and some key issues