Social network analysis is:

1. Introduction • Social network analysis is: • a set of relational methods for systematically understanding and identifying connections among actors

2. Basic concepts Network Components • Actors (nodes, points, vertices): • - Individuals, Organizations, Events … • Relations (lines, arcs, edges, ties): between pairs of actors. • - Undirected (symmetric) / Directed (asymmetric) • - Binary / Valued

3. Basic concepts Types of network data: • 1) Egocentered Networks • Data on a respondent (ego) and the people they are connected to. Measures: Size Types of relations

4. Background Measures: Graph properties Density Sub-groups Positions Types of network data: • 2) Complete Networks • Connections among all members of a population. • Data on all actors within a particular (relevant) boundary. • Never exactly complete (due to missing data), but boundaries are set • Ex: Friendships among workers in a company.

5. b d a c e Social Network data The unit of interest in a network are the combined sets of actors and their relations. We represent actors with points and relations with lines. Example:

6. b d b b d d a c e a a c c e e Social Network data In general, a relation can be: Undirected / Directed Binary / Valued Directed, binary Undirected, binary b d 1 2 1 3 4 a c e Directed, Valued Undirected, Valued

7. a a b b c c d d e e b d b d a a 1 1 a c e a 1 1 c e b b 1 c c 1 1 1 1 1 1 d d 1 1 e e 1 1 1 1 Social Network data Basic Data Structures From pictures to matrices Undirected, binary Directed, binary

8. b f c e d Measuring Networks Connectivity Indirect connections are what make networks systems. One actor can reach another if there is a path in the graph connecting them. a b d a c e f

9. Measuring Networks Distance & number of paths Distance is measured by the (weighted) number of relations separating a pair, Using the shortest path. Actor “a” is: 1 step from 4 2 steps from 5 3 steps from 4 4 steps from 3 5 steps from 1 a

10. Measuring Networks An information network: Email exchanges within the Reagan white house, early 1980s (source: Blanton, 1995)

11. Measuring Networks Centrality Centrality refers to (one dimension of) location, identifying where an actor resides in a network. • Centrality is fairly straight forward: we want to identify which nodes are in the ‘center’ of the network. In the sense that they have many and important connections. • Three standard centrality measures capture a wide range of “importance” in a network: • Degree • Closeness • Betweenness

12. Measuring Networks Centrality The most intuitive notion of centrality focuses on degree. Degree is the number of lines, and the actor with the most lines is the most important:

13. Measuring Networks Centrality Degree Centrality: Relative measure of Degree Centrality:

14. Measuring Networks Centrality A second measure is closeness centrality. An actor is considered important if he/she is relatively close to all other actors. Closeness is based on the inverse of the distance of each actor to every other actor in the network. Closeness Centrality: Relative Closeness Centrality

15. Measuring Networks Centrality Closeness Centrality

16. Measuring Networks Centrality Betweenness Centrality: Model based on communication flow: A person who lies on communication paths can control communication flow, and is thus important. Betweenness centrality counts the number of shortest paths between i and k that actor j resides on. b a C d e f g h

17. Measuring Networks Centrality Betweenness centrality can be defined in terms of probability (1/gij), CB(pk) = iij(pk) = = gij = number of geodesics that bond actors pi and pj. gij(pk)= number of geodesics which bond pi and pj and content pk. iij(pk) = probability that actor pk is in a geodesic randomly chosen among the ones which join pi and pj. Betweenness centrality is the sum of these probabilities (Freeman, 1979). Normalizad: C’B(pk) = CB(pk) / [(n-1)(n-2)/2]

18. Measuring Networks Centrality Betweenness Centrality:

19. Measuring Networks Centralization If we want to measure the degree to which the graph as a whole is centralized, we look at the dispersion of centrality: Freeman’s general formula for centralization (which ranges from 0 to 1):

20. Measuring Networks Centralization Degree Centralization Scores Freeman: .02 Freeman: 1.0 Freeman: 0.0

21. Measuring Networks Density The more actors are connected to one another, the more dense the network will be. Undirected network: n(n-1)/2 = 2n-1 possible pairs of actors. Δ = Directed network: n(n-1)*2/2 = 2n-2possible lines. ΔD =

22. Measuring Networks Density Freeman: .23 Freeman: .25 Freeman: 0.25

23. Social Network Software • UCINET • The Standard network analysis program, runs in Windows • Good for computing measures of network topography for single nets • Input-Output of data is a special 2-file format, but is now able to read PAJEK files directly. • Not optimal for large networks • Available from: • Analytic Technologies

24. Social Network Software • PAJEK • Program for analyzing and plotting very large networks • Intuitive windows interface • Started mainly a graphics program, but has expanded to a wide range of analytic capabilities • Can link to the R statistical package • Free • Available from: http://vlado.fmf.uni-lj.si/pub/networks/pajek/

25. Social Network Software • NetDraw • Also very new, but by one of the best known names in network analysis software. • Free