Social Network Analysis and Management Research

Report
Leeds University Business School
Introduction to Social Network
Analysis
Technology and Innovation Group
Leeds University Business School
Growing influence of SNA
SNA or "social network analysis" in Web of
science
500
400
300
No of hits
200
100
0
1985
1990
1995
2000
2005
2010
Year
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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.
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Development of SNA
Gestalt theory (1920-30s)
Structural – functional anthropology
Field theory, sociometry (30s)
Group dynamics
Graph theory (50s)
Manchester anthropologists (50-60s)
Harvard structuralists (60-70s)
Social network analysis (SNA) 80s
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adapted from
Scott (2000) p. 8
4
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
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Attributes vs. Relations
Attributes
ID
Actors/
Cases
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
Univariate
analysis
Correlations
Relations
(but not all
connections
shown)
Traditional analysis – focuses on attributes
SNA – focuses on relationships
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Relational matrix
A simple relational matrix in which presence/absence of a relation
is indicated by a 1 or 0 respectively: who drinks with whom?
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
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Sociograms
•
•
•
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
Tom
Sally
Alice
•
Attributes: nodes can have one or more attributes, e.g. gender, company;
seniority; tenure and job titles
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Basic network components
Triad
Dyad
Star (or wheel)
Clique (size 4)
Chain
Circle
centralised
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decentralised
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Directionality of ties
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
Tom
Fred
Tom
Dick
Tom
Sally
•e.g. Tom likes Sally and Sally likes Tom
•nodes connected by arcs/edges are also referred to as vertices
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Tie enumeration - binary
Ties might be present/ not present (binary) or can be valued
E.g. matrix shown earlier in which presence/absence of a relation is indicated
by a 1 or 0 respectively: who drinks with whom? .
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
Tom
Alice
Sally
Fred
Dick
Note matrix is symmetrical (and redundant) about diagonal
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Tie enumeration - valued
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.
To
Tom
From
Dick Sally
Fred
Alice
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
Note matrix is not symmetrical (nor redundant) about the diagonal
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Network – directed and valued
Tom
5
4
2
1
2
5
Dick
Sally
3
3
5
3
2
5
3
4
2
Alice
3
Fred
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Levels of measurement for ties
Directionality
Binary
Numeration
Valued
Undirected
Directed
1
3
2
4
Where 1 is lowest (simplest) level
Scott (2000) p. 47
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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
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Modes and matrices
Two mode – incidence matrix
Directors
Companies
A
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
B
W
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C
X
D
Y
E
Z
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Modes and matrices
Single mode – adjacency
matrix - company by directors
W
X
Y
Z
W
-
3
3
1
X
3
-
2
2
Y
3
2
-
1
Z
1
2
1
-
3
W
1
2
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
-
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2
3
Z
Single mode – adjacency
matrix – director by companies
X
Y
1
A
B
2
2
1
2
1
1
2
E
2
C
D
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Some network concepts
•
•
•
•
•
•
Degree
Distance, paths and diameter
Density
Centrality
Strong vs. weak ties
Holes and brokerage
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Degree
Degree: the number of other nodes that a node is directly connected to
Undirected ties
Tom
Dick
Sally
Fred
Alice
Tom
Tom
0
0
1
1
0
Dick
0
0
1
1
0
Sally
Fred
1
1
1
1
0
0
0
0
2
Alice
1
3 Sally
1
0
2
Fred
2
Dick
Alice
0
0
1
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0
0
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Degree for directed ties
To
Tom
Dick
Sally
Fred
Alice
Out-degree
Tom
0
2
1
5
4
4
Dick
0
0
3
0
4
2
2
5
0
3
5
4
3
2
2
0
8
4
Alice
5
3
3
0
0
3
Indegree
3
4
4
2
4
17
F
r Sally
o
Fred
m
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Distance, paths and diameter
•
Path and distance both measured by ‘degree’ (i.e. links in the chain)
A
B
C
D
E.g. distance between A and D is 3
•
Diameter of a network: the shortest path between the two most distant
vertices in a network.
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Density
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
density 
l
n ( n  1) / 2
Low
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where
n = number of nodes
l = number of lines (ties)
HIgh
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Density
Scott (2000) p. 71
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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).
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Strong vs. weak ties
•
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
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Holes and brokerage
Bridge
Broker
If the bridge was not present there would be a
structural hole between the two parts of the network
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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
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Analysis focus
•node
•dyad
•whole network or components
•group vs. individual (egonet)
•network structure determines node attributes
•node attributes determine network structure
•etc.
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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
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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
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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
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Questions and discussion
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