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

2 Growing influence of SNA

Leeds University Business School 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), Boyd, D.M. & Ellison, N.B. (2008) Network sites: Definition, history and scholarship, Journal of Computer-Mediated Communication, 13(1), Hatala, J-P. (2006) Social network analysis in human resource development: a new methodology, Human Resource Development Review, 5(1) Ibarra, H. (1993) Network centrality, power, and innovation involvement: determinants of technical and administrative roles, Academy of Management Journal, 36(3), Reingen, P.H. & Kernan, J.B. (1986) Analysis of referral networks in marketing: methods and illustration, Journal of Marketing Research, 23, Tsai, W. (2000) Social capital, strategic relatedness and the formation of intraorganizational linkages, Strategic Management Journal, 21(9),

Leeds University Business School 4 Development of SNA Gestalt theory ( s)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

Leeds University Business School 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

Leeds University Business School 6 Attributes vs. Relations IDGenderAge (years) Height (m) Weight (kg) TomM DickM SallyF FredM AliceF Attributes Correlations Actors/ Cases Relations (but not all connections shown) Univariate analysis Traditional analysis – focuses on attributes SNA – focuses on relationships

Leeds University Business School 7 TomDickSallyFredAlice Tom00110 Dick00110 Sally11001 Fred11000 Alice00100 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

Leeds University Business School 8 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 Tom Sally Alice Sociograms

Leeds University Business School 9 Basic network components Dyad TriadClique (size 4) decentralisedcentralised Circle Star (or wheel)Chain

Leeds University Business School 10 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 TomFred TomDick TomSally

Leeds University Business School 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?. TomDickSallyFredAlice Tom00110 Dick00110 Sally11001 Fred11000 Alice00100 Tom Dick Fred Sally Alice Note matrix is symmetrical (and redundant) about diagonal

Leeds University Business School 12 Tie enumeration - valued TomDickSallyFredAlice Tom02154 Dick00304 Sally25035 Fred32208 Alice53300 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

Leeds University Business School 13 Network – directed and valued

Leeds University Business School UndirectedDirected Binary Valued Directionality Numeration Scott (2000) p. 47 Levels of measurement for ties Where 1 is lowest (simplest) level

Leeds University Business School 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

Leeds University Business School 16 Modes and matrices ABCDE W11110 X11101 Y01110 Z00101 Two mode – incidence matrix Directors Companies ABCDE WXYZ

Leeds University Business School 17 Modes and matrices WXYZ W-331 X3-22 Y32-1 Z121- ABCDE A-2211 B2-321 C23-22 D122-0 E1120- Single mode – adjacency matrix - company by directors Single mode – adjacency matrix – director by companies W X YZ AB C D E

Leeds University Business School 18 Some network concepts Degree Distance, paths and diameter Density Centrality Strong vs. weak ties Holes and brokerage

Leeds University Business School 19 Degree Tom Dick Fred Sally Alice Degree: the number of other nodes that a node is directly connected to Undirected ties TomDickSallyFredAlice Tom00110 Dick00110 Sally11001 Fred11000 Alice00100

Leeds University Business School 20 TomDickSallyFredAliceOut-degree Tom Dick Sally Fred Alice In- degree FromFrom To Degree for directed ties

Leeds University Business School 21 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 BCD E.g. distance between A and D is 3

Leeds University Business School 22 Density 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

Leeds University Business School 23 Density Scott (2000) p. 71

Leeds University Business School 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).

Leeds University Business School 25 Mark Granovetter (1973) The strength of weak ties American Journal of Sociology 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

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

Leeds University Business School 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

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

Leeds University Business School 29 Some SNA Literature Borgatti, S.P., Mehra, A., Brass, D.J. and Labianca, G. (2009) Network analysis in the social sciences, Science, 323, 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

Leeds University Business School 30 SNA software UCINET Pajek Egonet See list on International Network for Social Network Analysis (INSNA) website

Leeds University Business School 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:

Leeds University Business School 32 Questions and discussion