Introduction to Social Network Analysis

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

2. Growing influence of SNA

3. 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.

4. 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) adapted from Scott (2000) p. 8 Social network analysis (SNA) 80s

5. 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

6. Attributes vs. Relations Attributes Actors/Cases Relations (but not all connections shown) Univariate analysis Correlations Traditional analysis – focuses on attributes SNA – focuses on relationships

7. 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?

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

9. Basic network components Triad Clique (size 4) Dyad Star (or wheel) Chain Circle centralised decentralised

10. 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 • e.g. Tom likes Sally and Sally likes Tom • nodes connected by arcs/edges are also referred to as vertices Tom Fred Tom Dick Tom Sally

11. 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 Alice Sally Fred Dick Note matrix is symmetrical (and redundant) about diagonal

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

13. Network – directed and valued

14. Levels of measurement for ties Directionality Undirected Directed Binary Numeration Valued Where 1 is lowest (simplest) level Scott (2000) p. 47

15. 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

16. Modes and matrices Two mode – incidence matrix A B C D E Directors Companies W X Y Z

17. Modes and matrices Single mode – adjacency matrix - company by directors 3 W X 1 2 2 3 Z Y 1 Single mode – adjacency matrix – director by companies A B 2 2 1 2 1 1 2 E C 2 D

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

19. Degree Degree: the number of other nodes that a node is directly connected to Undirected ties Tom 2 Alice Sally 1 3 2 Fred 2 Dick

20. Degree for directed ties To From

21. 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.

22. 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 where n = number of nodes l = number of lines (ties) HIgh Low

23. Density Scott (2000) p. 71

24. 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).

25. 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

26. Holes and brokerage Bridge Broker If the bridge was not present there would be a structural hole between the two parts of the network

27. 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

28. Analysis focus • node • dyad • whole network or components • group vs. individual (egonet) • network structure determines node attributes • node attributes determine network structure • etc.

29. 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

30. SNA software • UCINET http://www.analytictech.com/ucinet/ • Pajekhttp://pajek.imfm.si/doku.php • Egonethttp://sourceforge.net/projects/egonet/ • See list on International Network for Social Network Analysis (INSNA) website http://www.insna.org/sna/links.html

31. 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

32. Questions and discussion