Pajek Workshop Vladimir Batagelj Andrej Mrvar Wouter de
Pajek Workshop Vladimir Batagelj Andrej Mrvar Wouter de Nooy Sunbelt XXIV, Portorož, 2004 1
Today’s Program • Introduction to Pajek and social network analysis • Analysing large networks with Pajek and fine-tuning layouts • Discussion and questions Sunbelt XXIV, Portorož, 2004 2
PART 1 Exploratory Network Analysis ž with Pajek (Published at Cambridge University Press, October 2004) W. de Nooy, A. Mrvar, V. Batagelj Sunbelt XXIV, Portorož, 2004 3
Overview • Network data • Ranking: – prestige • Vertex attributes and – acyclic networks properties • Cohesive subgroups: • Blockmodeling – in simple networks • Networks and time – in signed networks – in valued networks • Brokerage: – centrality – structural holes – brokerage roles – repeated measurement – diffusion – genealogies, citations • Network analysis and statistics • Building your own Sunbelt XXIV, Portorož, 2004 4
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 5
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 6
Cohesive subgroups in simple networks • Connectivity • Example: Attiro. paj • Measures: – Components: weak and strong – k-cores – Cliques, complete subnetworks • Analytic strategy Sunbelt XXIV, Portorož, 2004 7
Sunbelt XXIV, Portorož, 2004 8
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 9
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 Sunbelt XXIV, Portorož, 2004 10
Centrality • Centrality and centralization • Undirected networks (Knoke & Burt, 1983) • Example: Strike. paj – Degree – Closeness – Betweenness Sunbelt XXIV, Portorož, 2004 11
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 12
5 Brokerage roles Sunbelt XXIV, Portorož, 2004 13
Prestige • Asymmetric choices • Example: San. Juan. Sur 2. 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 14
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 15
Balance-theoretic models Sunbelt XXIV, Portorož, 2004 16
Triad types and models Sunbelt XXIV, Portorož, 2004 17
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 18
Cohesive subgroups Sunbelt XXIV, Portorož, 2004 19
Image matrix Class Spanish English – young Spanish Complete Empty English – young Empty Complete Empty English – old Empty Complete Sunbelt XXIV, Portorož, 2004 English – old 20
Blockmodel types Sunbelt XXIV, Portorož, 2004 21
Regular equivalence and errors Sunbelt XXIV, Portorož, 2004 22
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: Mod. Math. 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 23
Genealogies • Data format: GEDCOM 5. 5 standard www. gendex. com/gedcom 55/55 gcint. htm • Software: - Genealogical Information Manager www. mind spring. com/~dblaine/gim home. html - Personal Ancestral File www. familysearch. org Sunbelt XXIV, Portorož, 2004 24
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 25
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 26
Relations among chapters Sunbelt XXIV, Portorož, 2004 27
- Slides: 27