Pajek Workshop

1. Pajek Workshop Vladimir Batagelj Andrej Mrvar Wouter de Nooy Sunbelt XXIV, Portorož, 2004

2. Today’s Program • Introduction to Pajek and social network analysis • Analysing large networks with Pajekand fine-tuning layouts • Discussion and questions Sunbelt XXIV, Portorož, 2004

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

4. 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 Overview Sunbelt XXIV, Portorož, 2004

5. 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 Sunbelt XXIV, Portorož, 2004

6. 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 Sunbelt XXIV, Portorož, 2004

7. Cohesive subgroupsin simple networks • Connectivity • Example: Attiro.paj • Measures: • Components: weak and strong • k-cores • Cliques,complete subnetworks • Analytic strategy Sunbelt XXIV, Portorož, 2004

8. Sunbelt XXIV, Portorož, 2004

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 Sunbelt XXIV, Portorož, 2004

10. Cohesive subgroupsin 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 Sunbelt XXIV, Portorož, 2004

11. Centrality • Centrality and centralization • Undirected networks (Knoke & Burt, 1983) • Example: Strike.paj • Degree • Closeness • Betweenness Sunbelt XXIV, Portorož, 2004

12. 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 Sunbelt XXIV, Portorož, 2004

13. 5 Brokerage roles Sunbelt XXIV, Portorož, 2004

14. 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 Sunbelt XXIV, Portorož, 2004

15. 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 Sunbelt XXIV, Portorož, 2004

16. Balance-theoretic models Sunbelt XXIV, Portorož, 2004

17. Triad types and models Sunbelt XXIV, Portorož, 2004

18. 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 Sunbelt XXIV, Portorož, 2004

19. Cohesive subgroups Sunbelt XXIV, Portorož, 2004

20. Image matrix Sunbelt XXIV, Portorož, 2004

21. Blockmodel types Sunbelt XXIV, Portorož, 2004

22. Regular equivalence and errors Sunbelt XXIV, Portorož, 2004

23. 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 Sunbelt XXIV, Portorož, 2004

24. 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 Sunbelt XXIV, Portorož, 2004

25. 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 Sunbelt XXIV, Portorož, 2004

26. 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 Sunbelt XXIV, Portorož, 2004

27. Relations among chapters Sunbelt XXIV, Portorož, 2004