1. Sunbelt XXIV, Portorož, 20041 Pajek Workshop Vladimir Batagelj Andrej Mrvar Wouter de Nooy

2. Sunbelt XXIV, Portorož, 20042 Today’s Program Introduction to Pajek and social network analysis Analysing large networks with Pajek and fine-tuning layouts Discussion and questions

3. Sunbelt XXIV, Portorož, 20043 PART 1 Exploratory Network Analysis with Pajek (Published at Cambridge University Press, October 2004) W. de Nooy, A. Mrvar, V. Batagelj ž

4. Sunbelt XXIV, Portorož, 20044 Overview Network data Vertex attributes and properties Cohesive subgroups: –in simple networks –in signed networks –in valued networks Brokerage: –centrality –structural holes –brokerage roles Ranking: –prestige –acyclic networks Blockmodeling Networks and time –repeated measurement –diffusion –genealogies, citations Network analysis and statistics Building your own

5. Sunbelt XXIV, Portorož, 20045 Network data Opening a network in Pajek Drawing a network in Pajek –Energizing the layout –Selecting display options –Exporting the sociogram Pajek network data –Structure –Store & export from Access Example: World trade relations –Imports_manufactures.net

6. Sunbelt XXIV, Portorož, 20046 Vertex attributes and structural properties Types of data objects –Partitions: discrete properties –Clusters: 1 class from a partition –Vectors: continuous (numeric) properties –Hierarchies: nested classification –Permutations: reordering (renumbering) Visualizing partitions and vectors Menu structure Pajek project file

7. Sunbelt XXIV, Portorož, 20047 Cohesive subgroups in simple networks Connectivity Example: Attiro.paj Measures: –Components: weak and strong –k-cores –Cliques, complete subnetworks Analytic strategy

8. Sunbelt XXIV, Portorož, 20048

9. 9 Cohesive subgroups in signed networks Balanced clusters Example: Sampson.paj Using line values & signs in layout Optimization approach –Set parameters –Search optimal solution –Repeat many times Stepping through partitions

10. Sunbelt XXIV, Portorož, 200410 Cohesive subgroups in valued networks Cohesion by strong or multiple ties Example: interlocking directorates in Scottish banking (circa 1900) Scotland.paj Transform 2-mode into 1-mode network Measure: –m-core (valued core) SVG output

11. Sunbelt XXIV, Portorož, 200411 Centrality Centrality and centralization Undirected networks (Knoke & Burt, 1983) Example: Strike.paj –Degree –Closeness –Betweenness

12. Sunbelt XXIV, Portorož, 200412 Brokerage The flow of information Example: Strike.paj Overall network structure: –Bridges –Cut-vertices or articulation points –Bi-components Investigating the ego-network: –Structural holes –Brokerage roles

13. Sunbelt XXIV, Portorož, 200413 5 Brokerage roles

14. Sunbelt XXIV, Portorož, 200414 Prestige Asymmetric choices Example: SanJuanSur2.paj Measures: –Popularity: indegree –Input domain: direct and indirect nominations –Proximity prestige: size of domain divided by the average distance within the domain Structural and social prestige

15. Sunbelt XXIV, Portorož, 200415 Ranks: acyclic networks Discrete ranks or levels Example: student_government.paj Local network structure: –Triadic analysis and the triad census Overall network structure: –Strong components and ranks –Symmetric-acyclic decomposition

16. Sunbelt XXIV, Portorož, 200416 Balance-theoretic models

17. Sunbelt XXIV, Portorož, 200417 Triad types and models

18. Sunbelt XXIV, Portorož, 200418 Blockmodeling Matrix and permutation for visualization Blockmodel –Partition of vertices into classes (positions) –Image matrix of relations among blocks Types of blockmodels –Cohesive subgroups –Center-periphery structure –Ranks Types of equivalence: –Structural equivalence: hierarchical clustering –Regular equivalence

19. Sunbelt XXIV, Portorož, 200419 Cohesive subgroups

20. Sunbelt XXIV, Portorož, 200420 Image matrix ClassSpanish English – young English – old SpanishCompleteEmpty English – young EmptyCompleteEmpty English – old Empty Complete

21. Sunbelt XXIV, Portorož, 200421 Blockmodel types

22. Sunbelt XXIV, Portorož, 200422 Regular equivalence and errors

23. Sunbelt XXIV, Portorož, 200423 Networks and time Longitudinal network: a network measured at different time points –Example: Sampson.paj Diffusion: vertex property changing over time, e.g., adoption –Example: ModMath.paj Descent: a relation spanning time –Genealogies: descent by birth; structural relinking –Citations: descent of ideas; main path analysis –Example: Gondola_Petrus.ged, centrality_literature.paj

24. Sunbelt XXIV, Portorož, 200424 Genealogies Data format: GEDCOM 5.5 standard www.gendex.com/gedcom55/55gcint.htm Software: - Genealogical Information Manager www.mind spring.com/~dblaine/gim home.html - Personal Ancestral File www.familysearch.org

25. Sunbelt XXIV, Portorož, 200425 Networks and statistics Statistical relations among properties of vertices: partitions and vectors Example: social and structural prestige (Ch. 9) In Pajek: discrete (Cramer’s V, Rajski, rank correlation) and continuous (Pearson correlation, regression) Pajek to R: see afternoon session Pajek to other statistics software: paste numbers from partition or vector into statistics software datasheet

26. Sunbelt XXIV, Portorož, 200426 Building your own Macro: sequences of commands performed on selected data objects Example: exposure in a diffusion network Macro commands: –Record –Add message: add comment –Play

27. Sunbelt XXIV, Portorož, 200427 Relations among chapters