social network analysis – introduction and some key issues social network analysis chris snijders...

Social network analysis – introduction and some key issues

Social network analysis

Chris Snijders

Dept of Technology Management

Cap. group Technology & Policy

Eindhoven University of Technology

Eindhoven, The Netherlands

c.c.p.snijders@tm.tue.nl

[note: material partly collected online!]

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

Brief introduction to social network analysis

"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. MorenoNew York Times, April 13, 1933

We live in a 'social space'

“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

We live in a connected world

Example network (source: Borgatti)

Example network: a food “chain”

Why do networks matter?

“practical classics”

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

•…

The network perspective

Two firms in the same market.

Which firm performs better (say, more innovative): A or B?

AND … POSITION IN THE NETWORK OF FIRMS

Networks are one specific way of dealing with “market imperfection”

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.

Increasing popularity

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?

The International Network of Social Network Analysis (INSNA)

• Founded by Barry Wellman in 1976-1977– Sabbatical Travel Carried Tales– Nick Mullins: Every “Theory Group” Has an Organizational Leader– Owned by Wellman until 1988 as small business

• Subsequent Coordinators/Presidents– Al Wolfe, Steve Borgatti, Martin Everett

• Steering Committee• Non-Profit Constitution under Borgatti; Coordinator > President

– Bill Richards President, 2003-• Scott Feld VP; Katie Faust Treasurer; Frans Stokman, Euro. Rep.• Our First Real Election

• Grown from 175 to 400 Members• Many More on Listserv (Not Limited to Members)

– Steve Borgatti maintains; unmoderated

• Website: www.insna.org

The socnet-mailing list

***** To join INSNA, visit http://www.insna.org *****

Dear all,

Last week I asked about designing a survey form to gather SNA 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

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

Some key social network books

1) Elizabeth Bott, Family & Social Network, 1957

2) J. Clyde Mitchell, Networks, Norms & Institutions, 1973

3) Holland & Leinhardt, Perspectives on Social Network Research,1979s

4) S. D. Berkowitz, An Introduction to Structural Analysis, 1982

5) Knoke & Kuklinski, Network Analysis, 1983, Sage, low-cost

6) Charles Tilly, Big Structures, Large Processes, Huge Comparisons, 1984

7) Wellman & Berkowitz, eds., Social Structures, 1988

8) David Knoke, Political Networks, 1990

9) John Scott, Social Network Analysis, 1991

10) Ron Burt, Structural Holes, 1992

11) Manuel Castells, The Rise of Network Society, 1996, 2000

12) Wasserman & Faust, Social Network Analysis, 1992

13) Nan Lin, Social Capital (monograph & reader), 2001

Social network software

1) UCINet – Many things on network analysis1) Lin Freeman, Steve Borgatti, Martin Everett

2) MultiNet – Whole Network Analysis 1) + Nodal Characteristics

3) Structure – Ron Burt – No longer maintained

4) P*Star – Dyadic Analysis – Stan Wasserman

5) Krackplot – Network Visualization (Obsolete)1) David Krackhardt, Jim Blythe

6) Pajek – Network Visualization – Supersedes Krackplot

7) StocNet – Tom Snijders - collected programs for, e.g., analysis of dynamic networks

Kinds of data collection through SNA history

• Small Group “Sociometry”1930s > (Moreno, Bonacich, Cook)– 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

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

The basics: what is a network

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)

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

Example network: Collaboration between disciplines (source: Borgatti)

Example network: terrorists (source: Borgatti)

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

Some typical research questions in social network analysis

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”)

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”)

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?

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

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.”

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

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

… … …

Network concepts

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

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- …

Network representations: graph and matrix

A 1-mode, non-valued, directed network

A B C D

A - 1 1 0

B 0 - 0 0

C 0 1 - 1

D 0 0 0 -

A B C D

A - 9 4 0

B 9 - 1 0

C 4 1 - 3

D 0 0 3 -

A 1-mode, non-valued, undirected network

Kinds of network data

AND another dimension: directed relations or undirected

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 / sociometryAlgebraic 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?

Some network concepts

gets from A to X:

A-C-A-D-F-X

Walk, but without repeating lines:

A-D-E-F-D-B-X

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

More network concepts

XCutpoints

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.

Individual Network Measures

• Degree: Percentage of ties to the other actors an actor has (in directed graphs: InDegree and OutDegree)

• Degree quality: Percentages of tiesto 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

A - 1 1 0

B 0 - 0 0

C 0 1 - 1

D 0 0 0 -

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?)

About network literature

Make sure you talk about network embeddedness

Single actorproperties determine behavior

Dyad+ properties of

partner and relation determine behavior

Network+ network

properties determine behavior

Temporal embeddedness

Network embeddedness

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.

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 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

Research classic:

Granovetter’s (1973)

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

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

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

ties17% 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

Mark Granovetter:other work

Granovetter is well known for the notion of “(social) embeddedness”: all behavior occurs in a social structure, and that structure

hasinfluence on behavior.

Institutional embeddedness: shared rules and normsexample: 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 notexample: two firms in an alliance who anticipate future dealings, vs not

Structural embeddedness: the existence of relations with third partiesexample: two firms in an alliance have mutual customers, vs not

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

Research classic:

Burt’s (1988)

“Structural holes” as a response to Coleman’s closure argument

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 organization

Robert

“Structural holes create value”

Robert will do better than James, because of:

-informational benefits

-“tertius gaudens” (entrepreneur)

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

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.

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 …?

Research classic:

The “small world phenomenon” and theoretical research into social networks

Or: one typical kind of network structure

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

The small world phenomenon (cont.)

• “Small world project” is testing this assertion as we speak (http://smallworld.columbia.edu), you can still participate

• Email to <address>, otherwise same rules. Addresses were American college professor, Indian technology consultant, Estonian archival inspector, …

• Conclusion:– Low completion rate (384 out of 24163 = 1.5%) – Succesful chains more often through professional ties– Succesful chains more often through weak ties (weak ties

mentioned about 10% more often)– Chain size 5, 6 or 7.

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”

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]

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: 2.77Al Pacino: 2.87 [AS -> Charlton Heston -> MD]

Combining game theory and networks – Axelrod (1980), Watts & Strogatz (1989)

[neural network of some wurm, power grid of electricity net, actor network]

1. Consider a given network.

2. All connected actors play the repeated Prisoner’s Dilemma for some rounds. [indefinite vs definite]

3. After a given number of rounds, the strategies “reproduce” in the sense that the proportion of the more succesful strategies increases in the network, whereas the less succesful strategies decrease or die

4. Repeat 2 and 3 until a stable state is reached.

5. Conclusion: to sustain cooperation, you need a short average distance, and cliquishness (“small worlds”)

Collecting and analyzing network data

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?)

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)

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)

• 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?”

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”

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)

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)

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)

Literature and readings

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)

PeriodicalsSocial Networks: An International Journal of Structural Analysis (1978-present). Edited byLinton C. Freeman and Ronald L. Breiger. Many of the more technical, methodsorientedarticles about networks appear here. Available on-line through HOLLISbeginning in 1995; see http://lib.harvard.edu/e-resources/details/s/socnetwk.html(requires Harvard ID and PIN for access).

Connections (1977-present). Edited by William D. Richards and Thomas W. Valente.Newsletter of the International Network for Social Network Analysis (INSNA).[Subscription carries membership in INSNA; see http://www.sfu.ca/~insna forinformation. Web version of CONNECTIONS is available six months after hardcopypublication at the same Web address.]

Journal of Social Structure (2000-present). Edited by David Krackhardt. An electronic journalpublishing a variety of work on social networks, some of which uses display options notavailable for print journals. Available free of charge athttp://www.heinz.cmu.edu/project/INSNA/joss/index1.html.

Books providing overviews:Berkowitz, S.D. 1982. An Introduction to Structural Analysis: The Network Approach to SocialResearch. Toronto: Butterworth’s.Degenne, Alain and Michel Forsé. 1999. Introducing Social Networks. Thousand Oaks, CA:Sage Publications.Knoke, David. 1990. Political Networks: The Structural Perspective. New York: CambridgeUniversity Press.Knoke, David and James H. Kuklinski. 1982. Network Analysis. Beverly Hills: Sage.Monge, Peter R. and Noshir S. Contractor. 2003. Theories of Communication Networks. NewYork: Oxford University Press.

Literature & readingsCollections:

Burt, Ronald S. and Michael J. Minor (eds.). 1983. Applied Network Analysis: AMethodological Introduction. Beverly Hills: Sage. [collection of basic methods articles.]Doreian, Patrick and Frans N. Stokman, eds. Evolution of Social Networks. Special issues ofthe 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 Methodsin Social Network Analysis. Fairfax, VA: George Mason University Press. [collection ofcomparatively 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 andLiability. Boston: Kluwer Academic Publishers. [collection of recent articles on socialcapital 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 andcommunities, presented at a 1998 conference.]Lin, Nan, Alfred Dean and Walter Ensel. 1986. Social Support, Life Events, and Depression.New York: Academic Press.Marsden, Peter V. and Nan Lin (eds.). 1982. Social Structure and Network Analysis. BeverlyHills: Sage. [collection of substantively-focused articles from 1981 conference]Mitchell, J. Clyde (ed.). 1969. Social Networks in Urban Situations. Manchester, UK:Manchester University Press [collection of conceptual articles and applications, based onthe British social anthropological tradition]Mizruchi, Mark S. and Michael Schwartz (eds.). 1987. Intercorporate Relations: The StructuralAnalysis of Business. New York: Cambridge University Press. [collection of papers oninterlocking directorates, class cohesion, etc.]Wasserman, Stanley, and Joseph Galaskiewicz (eds.) 1994. Advances in Social NetworkAnalysis: Research in the Social and Behavioral Sciences. Newbury Park, CA: SagePublications. [1990s stock-taking of what has been learned from the network approach inseveral fields of application.]

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 andcommunities.]Wellman, Barry and S.D. Berkowitz (eds.). 1988. Social Structures: A Network Approach.New York: Cambridge University Press. [collection of conceptual and substantivearticles 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 largelyexperimental 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: CambridgeUniversity Press.Granovetter, Mark S. 1995. Getting a Job: A Study of Contacts and Careers. Second Edition(first published in 1974). Chicago: University of Chicago Press.Knoke, David, Franz Urban Pappi, Jeffrey Broadbent and Yutaka Tsujinaka. 1996. ComparingPolicy Networks: Labor Politics in the U.S., Germany, and Japan. New York:Cambridge University Press.Laumann, Edward O. and David Knoke. 1987. The Organizational State: Social Choice inNational Policy Domains. Madison, WI: University of Wisconsin Press.Lin, Nan. 2001. Social Capital: A Theory of Social Structure and Action. New York:Cambridge University Press.Valente, Thomas W. 1995. Network Models of the Diffusion of Innovations. Cresskill, NJ:Hampton Press.

Watts, Duncan J. 1999. Small Worlds: The Dynamics of Networks between Order andRandomness. 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: StateUniversity 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 RhondaJ.V. Montgomery (eds.) Encyclopedia of Sociology. Second edition. New York:MacMillan.Marsden, Peter V. (forthcoming) “Network Analysis”, to appear in Kimberly Kempf-Leonard(ed.) Encyclopedia of Social Measurement. San Diego, CA: Academic Press.

Egocentric Networks, Measurement, and “Social Capital”Wasserman and Faust, chapter 2.Scott, chapter 3.Marsden, Peter V. 1990. "Network Data and Measurement." Annual Review of Sociology 16:435-463.Marsden, Peter V. (forthcoming) “Recent Developments in Network Measurement.” To appearin Peter J. Carrington, John Scott, and Stanley Wasserman, Models and Methods inSocial Network Analysis. New York: Cambridge University Press.Marsden, Peter V. 1987. "Core Discussion Networks of Americans." American SociologicalReview 52: 122-131.Burt, Ronald S. 1997. “The Contingent Value of Social Capital.” Administrative ScienceQuarterly 42: 339-365.

Whole Networks; Introduction to Graph TheoryWasserman and Faust, chapters 3-4.Scott, chapter 4.

Centrality and CentralizationWasserman and Faust, chapter 5.Scott, chapter 5.Freeman, Linton C. 1979. "Centrality in Social Networks: I. Conceptual Clarification." SocialNetworks 1: 215-239.Bonacich, Phillip. 1987. “Power and Centrality: A Family of Measures.” American Journal ofSociology 92: 1170-1182.Brass, Daniel. 1984. “Being in the Right Place: A Structural Analysis of Individual Influence inan Organization.” Administrative Science Quarterly 29: 518-539.Faust, Katherine. 1997. “Centrality in Affiliation Networks.” Social Networks 19: 157-191.

Subgroups in Networks, I: Cohesive SubgroupsWasserman and Faust, chapter 7.Scott, chapter 6Bartholomew, David J., Fiona Steele, Irini Moustaki, and Jane I. Galbraith. 2002. The Analysisand Interpretation of Multivariate Data for Social Scientists. London: Chapman andHall/CRC. Chapter 2 (“Cluster Analysis”).Freeman, Linton C. 1992. “The Sociological Concept of ‘Group’: An Empirical Test of TwoModels.” American Journal of Sociology 98: 152-166.Frank, Kenneth A. 1995. “Identifying Cohesive Subgroups.” Social Networks 17: 27-56.Moore, Gwen. 1979. “The Structure of a National Elite Network.” American SociologicalReview 44: 673-692.Krackhardt, David. 1999. "The Ties That Torture: Simmelian Tie Analysis in Organizations."Research in the Sociology of Organizations, 16:183-210.

Subgroups in Networks, II: Blockmodels/Positional Analysis Wasserman and Faust, chapters 9, 10.Scott, chapter 7White, Harrison C., Scott A. Boorman and Ronald L. Breiger. 1976. “Social Structure fromMultiple Networks. I. Blockmodels of Roles and Positions.” American Journal ofSociology 81: 730-779.9Borgatti, Stephen P. and Martin G. Everett. 1992. "Notions of Position in Social NetworkAnalysis." 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 NetworksScott, Social Network Analysis, Chapter 8.Freeman, Linton C. 2000. “Visualizing Social Networks.” Journal of Social Structure 1.Electronically available at http://www.heinz.cmu.edu/project/INSNA/joss/.Bartholomew et al., The Analysis and Interpretation of Multivariate Data for Social Scientists.Chapters 3 (“Multidimensional Scaling”) and 4 (“Correspondence Analysis”)Krackhardt, David, Jim Blythe and Cathleen McGrath. 1994. “KrackPlot 3.0: An ImprovedNetwork Drawing Program.” Connections 17: 53-55.Laumann, Edward O. and Franz U. Pappi. 1973. “New Directions in the Study of CommunityElites.” American Sociological Review 38: 212-230.McGrath, Cathleen, Jim Blythe, and David Krackhardt. 1997. “The Effect of SpatialArrangement on Judgments and Errors in Interpreting Graphs.” Social Networks 19:223-242.

Analyzing and Representing “Two-Mode” Network DataWasserman and Faust, chapter 8Breiger, 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.” SocialNetworks 19: 243-269.Bearden, James and Beth Mintz. 1987. “The Structure of Class Cohesion: The CorporateNetwork and Its Dual.” Pp. 187-207 in Mark S. Mizruchi and Michael Schwartz (eds.)Intercorporate Relations: The Structural Analysis of Business. New York: CambridgeUniversity 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: LogitModels for Social Networks.” Social Networks 21: 37-66.Crouch, Bradley and Stanley Wasserman. 1997. “A Practical Guide to Fitting p* SocialNetwork Models Via Logistic Regression.” Connections 21: 87-101. (Download versionavailable at p* website, see below.)Wasserman, Stanley, and Philippa Pattison. 1996. “Logit models and logistic regressions forsocial networks: I. An introduction to Markov graphs and p*.” Psychometrika, 60: 401-426.

Skvoretz, John and Katherine Faust. 1999. “Logit Models for Affiliation Networks.” Pp. 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 http://kentucky.psych.uiuc.edu/pstar/

Comparing Networks Hubert, Lawrence J. and Frank B. Baker. 1978. “Evaluating the Conformity of SociometricMeasurements.” Psychometrika 43: 31-41.Baker, Frank B. And Lawrence J. Hubert. 1981. “The Analysis of Social Interaction Data: ANonparametric 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, Sizeand Species.” Pp. 267-299 in Ross M. Stolzenberg (ed.) Sociological Methodology2002. Boston, MA: Blackwell Publishing.

Cognitive Social Structure DataKrackhardt, David. 1987. “Cognitive Social Structures.” Social Networks 9: 109-134.Kumbasar, Ece, A. Kimball Romney and William H. Batchelder. 1994. “Systematic Biases inSocial Perception.” American Journal of Sociology 100: 477-505.Krackhardt, David 1990. “Assessing the Political Landscape: Structure, Cognition, and Power inOrganizations.” Administrative Science Quarterly 35: 342-369.

Models for Studying Network Effects and DiffusionMarsden, Peter V. and Noah E. Friedkin. 1994. "Network Studies of Social Influence." Pp. 3-25in Wasserman and Galaskiewicz (eds.) Advances in Social Network Analysis.Ibarra, Herminia and Steven B. Andrews. 1993. “Power, Social Influence, and Sense-Making:Effects of Network Centrality and Proximity on Employee Perceptions.” AdministrativeScience Quarterly 38: 277-304.Hedström, Peter, Rickard Sandell and Charlotta Stern. 2000. “Mesolevel Networks and theDiffusion of Social Movements: The Case of the Swedish Social Democratic Party.”American Journal of Sociology 106: 145-172.Strang, David and Nancy Brandon Tuma. 1993. “Spatial and Temporal Heterogeneity inDiffusion.” American Journal of Sociology 99: 614-639.Morris, Martina. 1994. “Epidemiology and Social Networks: Modeling Structured Diffusion.”Pp. 26-52 in Wasserman and Galaskiewicz (eds.) Advances in Social Network Analysis.

Longitudinal Network Analysis11Snijders, Tom A.B. 1996. “Stochastic Actor-Oriented Models for Network Change.” Journal ofMathematical Sociology 21: 149-172.Van de Bunt, Gerhard G., Marijte A.J. van Duijn and Tom A.B. Snijders. 1999. “FriendshipNetworks Through Time: An Actor-Oriented Statistical Network Model.”Computational and Mathematical Organization Theory 5: 167-192.

Network SamplingScott, chapter 3 (end)Granovetter, Mark. 1976. “Network Sampling: Some First Steps.” American Journal ofSociology 81: 1287-1303.Frank, Ove. 1978. “Sampling and Estimation in Large Social Networks.” Social Networks 1:91-101.Klovdahl, Alden S., Z. Dhofier, G. Oddy, J. O’Hara, S. Stoutjesdijk, and A. Whish. 1977.“Social Networks in an Urban Area: First Canberra Study.” Australian and New ZealandJournal of Sociology 13: 169-172.

Network measures

Dealing with your data

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: …

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?

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

WE TAKE: [2]

uid n1 n2 … n31

1 9 2 … 3

2 4 9 … 1

3 1 1 … 4

… … … … …

31 2 1 … 9

TO GET: [3]

uid Measure

1 0.12

2 0.34

3 0.25

… …

31 0.94

… WE THEN MERGE [3] TO [1] ON <uid>,

AND RUN AN ANALYSIS IN SPSS ON THE MERGED FILES

through Ucinet

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 separatelyNOTE2: this gives rise to several global network measures, such as (in/out)degree varianceNOTE3: 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!

Network measures (2): number of ties of a certain quality

1 = do not even know this firm2 = have heard of this firm, have never dealt with it3 = know this firm, have dealt with it once or twice4 = have dealt with this firm regularly5 = 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

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

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

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!

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

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

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)

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

WE TAKE: [2]

uid n1 n2 … n31

1 9 2 … 3

2 4 9 … 1

3 1 1 … 4

… … … … …

31 2 1 … 9

TO GET: [3]

uid Measure

1 0.12

2 0.34

3 0.25

… …

31 0.94

… WE THEN MERGE [3] TO [1] ON <uid>,

AND RUN AN ANALYSIS IN SPSS ON THE MERGED FILES

through Ucinet

A brief view on Ucinet

Importing data using DL-files -----------------------

dl n=31

Labels:

A B … Z

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:

<name>.##h

<name>.##d

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

Some final issues

General issues in social network analysis

• Think carefully about what defines an actor (often simple) and what defines a tie (often complicated)

• Always think carefully about which property of the network it is, that drives the effect (closeness, betweenness, density, something else)

• Think beforehand about how to tackle the data, and build in proxies in the data collection. Using (only) directly measured network data is risky.

• When it comes to statistics, know that network data have their own typical problems that sometimes cannot (yet) be solved with standard SPSS-like packages.

• There is still something to gain here for researchers: network research is still in its infancy.

• We have just created a “weak tie”. If you have any questions related to social networks, ask! (c.c.p.snijders@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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