Leeds University Business School Introduction to Social Network Analysis Technology and Innovation Group Leeds University Business School

Leeds University Business School

Introduction to Social Network Analysis

Technology and Innovation Group

Leeds University Business School

Leeds University Business School2

1985 1990 1995 2000 2005 20100

100

200

300

400

500

SNA or "social network analysis" in Web of science

Year

No of hits

Growing influence of SNA


Example applications within management and business

• Borgatti, S.P. & Cross, R. (2003) A relational view of information seeking and learning in social networks, Management Science, 49(4), 432-445.

• Boyd, D.M. & Ellison, N.B. (2008) Network sites: Definition, history and scholarship, Journal of Computer-Mediated Communication, 13(1), 210-230.

• Hatala, J-P. (2006) Social network analysis in human resource development: a new methodology, Human Resource Development Review, 5(1) 45-71

• Ibarra, H. (1993) Network centrality, power, and innovation involvement: determinants of technical and administrative roles, Academy of Management Journal, 36(3), 471-501.

• Reingen, P.H. & Kernan, J.B. (1986) Analysis of referral networks in marketing: methods and illustration, Journal of Marketing Research, 23, 370-8.

• Tsai, W. (2000) Social capital, strategic relatedness and the formation of intraorganizational linkages, Strategic Management Journal , 21(9), 925-939.


Development of SNA

Gestalt theory (1920-30s) Structural – functional anthropology

Field theory, sociometry (30s)

Group dynamics

Graph theory (50s)

Social network analysis (SNA) 80s

Harvard structuralists (60-70s)

Manchester anthropologists (50-60s)

adapted from Scott (2000) p. 8


SNA – method or theory?

• “Social network analysis emerged as a set of methods for the analysis of social structures, methods that specifically allow an investigation of the relational aspects of these structures”

Scott (2000) p. 38

• “Social network theory provides an answer to a question that has preoccupied social philosophy from the time of Plato,… how autonomous individuals can combine to create enduring, functioning societies”

Borgatti et al. (2009) p.892


Attributes vs. Relations

ID Gender Age (years)

Height (m)

Weight (kg)

Tom M 30 1.85 115

Dick M 35 1.65 85

Sally F 25 1.60 65

Fred M 55 1.80 110

Alice F 45 1.70 70

Attributes

Correlations

Actors/Cases

Relations (but not all connections shown)

Univariate analysis

Traditional analysis – focuses on attributesSNA – focuses on relationships


Tom Dick Sally Fred Alice

Tom 0 0 1 1 0

Dick 0 0 1 1 0

Sally 1 1 0 0 1

Fred 1 1 0 0 0

Alice 0 0 1 0 0

A simple relational matrix in which presence/absence of a relation is indicated by a 1 or 0 respectively: who drinks with whom?

Relational matrix


• Nodes represent actors, e.g. people• Lines represent ties or relationships among actors, e.g. trust, information

sharing, friendship, etc.• Network is the structure of nodes and lines

• Attributes: nodes can have one or more attributes, e.g. gender, company; seniority; tenure and job titles

TomSally

Alice

Sociograms


Basic network components

Dyad Triad Clique (size 4)

decentralisedcentralised

Circle

Star (or wheel) Chain


Ties may be directed or undirected

• undirected lines (ties) are referred to as ‘edges’• e.g. Tom and Fred drink together

• directed lines are referred to as ‘arcs’ • direction is indicated by an arrow head (potentially at both ends)• e.g. Tom likes Dick but Dick doesn’t like Tom

• e.g. Tom likes Sally and Sally likes Tom

• nodes connected by arcs/edges are also referred to as vertices

Directionality of ties

Tom Fred

Tom Dick

Tom Sally


Tie enumeration - binary

Ties might be present/ not present (binary) or can be valuedE.g. matrix shown earlier in which presence/absence of a relation is indicated by a 1 or 0 respectively: who drinks with whom? .


Tom 0 0 1 1 0

Dick 0 0 1 1 0

Sally 1 1 0 0 1

Fred 1 1 0 0 0

Alice 0 0 1 0 0

Tom

Dick

FredSallyAlice

Note matrix is symmetrical (and redundant) about diagonal


Tie enumeration - valued


Tom 0 2 1 5 4

Dick 0 0 3 0 4

Sally 2 5 0 3 5

Fred 3 2 2 0 8

Alice 5 3 3 0 0

Ties can be valued (and in this case directed)E.g. may be weighted in ordinal/interval manner: e.g. 0 = ‘Don’t like’, 1=‘like’, 2=‘really like’; or telephones n times per week.

Note matrix is not symmetrical (nor redundant) about the diagonal

From

To


Tom

Fred

Dick

Sally

Alice

21

5

4

3

4

2

5

3 53

2

2

8

5

3

3

Network – directed and valued


1 3

2 4

Undirected Directed

Binary

Valued

Directionality

Numeration

Scott (2000) p. 47

Levels of measurement for ties

Where 1 is lowest (simplest) level


Different forms of tie

• Between individuals

• Between groups, organisations, etc.

• Similarities between actors, e.g. work in the same location, belong to same

groups, homophily

• Social relations, e.g. trust, friendship

• Interactions, e.g. attend same events

• Transactions, e.g. economic purchases, exchange information


Modes and matrices

A B C D E

W 1 1 1 1 0

X 1 1 1 0 1

Y 0 1 1 1 0

Z 0 0 1 0 1

Two mode – incidence matrix

Directors

Companies

A B C D E

W X Y Z


Modes and matrices

W X Y Z

W - 3 3 1

X 3 - 2 2

Y 3 2 - 1

Z 1 2 1 -

A B C D E

A - 2 2 1 1

B 2 - 3 2 1

C 2 3 - 2 2

D 1 2 2 - 0

E 1 1 2 0 -

Single mode – adjacency matrix - company by directors

Single mode – adjacency matrix – director by companies

W X

YZ

3

232

1

1

A B

C

D

E

22

21

11 2

2


Some network concepts

• Degree• Distance, paths and diameter• Density• Centrality• Strong vs. weak ties• Holes and brokerage


Degree

2

2

2

1 3

Tom

Dick

FredSallyAlice

Degree: the number of other nodes that a node is directly connected to

Undirected ties


Tom 0 0 1 1 0

Dick 0 0 1 1 0

Sally 1 1 0 0 1

Fred 1 1 0 0 0

Alice 0 0 1 0 0


Tom Dick Sally Fred

Alice Out-degree

Tom 0 2 1 5 4 4

Dick 0 0 3 0 4 2

Sally 2 5 0 3 5 4

Fred 3 2 2 0 8 4

Alice 5 3 3 0 0 3

In-degree

3 4 4 2 4 17

From

To

Degree for directed ties


• Path and distance both measured by ‘degree’ (i.e. links in the chain)

Distance, paths and diameter

• Diameter of a network: the shortest path between the two most distant vertices in a network.

A B C D

E.g. distance between A and D is 3


Density

2/)1(

nn

ldensity

where n = number of nodesl = number of lines (ties)

The actual number of connections in the network as a proportion of the total possible number of connections.

Calculated density is a figure between 0 and 1, where 1 is the maximum

Low HIgh


Density

Scott (2000) p. 71


Centrality

• Number of connections (degree centrality).

• Cumulative shortest distance to every other node in the graph (closeness centrality).

• Extent to which node lies in the path connecting all other nodes (betweenness centrality).


• Mark Granovetter (1973) The strength of weak ties American Journal of Sociology 78-1361-1381.

• The most beneficial tie may not always be the strong ones

• Strong ties are often connected to each other and are therefore sources of redundant information

Strong vs. weak ties


Holes and brokerage

BrokerBridge

If the bridge was not present there would be a structural hole between the two parts of the network


Data collection

• Questionnaire of group, e.g. roster• Interviews of group• Observation of group• Archival material, databases, etc.

• Sample size issues, e.g. need for high response rates• Symmetrisation• Ethical issues, e.g. assurance of confidentiality vs. discernible identification


Analysis focus

• node• dyad• whole network or components

• group vs. individual (egonet)

• network structure determines node attributes• node attributes determine network structure• etc.


Some SNA Literature

• Borgatti, S.P., Mehra, A., Brass, D.J. and Labianca, G. (2009) Network analysis in the social sciences, Science, 323, 892-895

• Freeman, L.C. (2004) The Development of Social Network Analysis: A Study in the Sociology of Science. Vancouver: Empirical Press.

• Scott, J. (2000) Social Network Analysis. London: Sage.• Wasserman, S. and Faust, K. (1994) Social Network Analysis: Methods

and Applications. Cambridge: Cambridge University Press


SNA software

• UCINET http://www.analytictech.com/ucinet/• Pajek http://pajek.imfm.si/doku.php• Egonet http://sourceforge.net/projects/egonet/• See list on International Network for Social Network

Analysis (INSNA) website http://www.insna.org/sna/links.html

http://www.analytictech.com/ucinet/

http://pajek.imfm.si/doku.php

http://sourceforge.net/projects/egonet/

http://www.insna.org/sna/links.html


SNA training and resources

• Essex Summer School• Hanneman, R.A. and Riddle, M. () Introduction to social

network methods – online text• De Nooy, W., Mrvar, A. and Batalgelj, V. (2005)

Exploratory social network analysis with Pajek, Cambridge University Press

• Various resources at: http://www.insna.org/sna/links.html

http://www.insna.org/sna/links.html


Questions and discussion

Documents

Leeds University Business School Introduction to Social Network Analysis Technology and Innovation Group Leeds University Business School