introduction to social network analysis
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Introduction to Social Network Analysis. Technology and Innovation Group Leeds University Business School. Growing influence of SNA. Example applications within management and business. - PowerPoint PPT PresentationTRANSCRIPT
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Leeds University Business School
Introduction to Social Network Analysis
Technology and Innovation GroupLeeds University Business School
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1985 1990 1995 2000 2005 20100
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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 AliceTom 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 matrixDirectors
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
211
1 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(
nnldensity where n = number of nodes
l = 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