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
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200
300
400
500
SNA or "social network analysis" in Web of science
Year
No of hits
Growing influence of SNA
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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)
Social network analysis (SNA) 80s
Harvard structuralists (60-70s)
Manchester anthropologists (50-60s)
adapted from Scott (2000) p. 8
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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
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
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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
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• 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
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Basic network components
Dyad Triad Clique (size 4)
decentralisedcentralised
Circle
Star (or wheel) Chain
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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
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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 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
Dick
FredSallyAlice
Note matrix is symmetrical (and redundant) about diagonal
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Tie enumeration - valued
Tom 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
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
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Tom
Fred
Dick
Sally
Alice
21
5
4
3
4
2
5
3 53
2
2
8
5
3
3
Network – directed and valued
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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
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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
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
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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
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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
2
2
2
1 3
Tom
Dick
FredSallyAlice
Degree: the number of other nodes that a node is directly connected to
Undirected ties
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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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
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• 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
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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
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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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• 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
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Holes and brokerage
BrokerBridge
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