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Pajek Workshop. Vladimir Batagelj Andrej Mrvar Wouter de Nooy. Today’s Program. Introduction to Pajek and social network analysis Analysing large networks with Pajek and fine-tuning layouts Discussion and questions. PART 1 Exploratory Network Analysis with Pajek

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pajek workshop

Pajek Workshop

Vladimir Batagelj

Andrej Mrvar

Wouter de Nooy

Sunbelt XXIV, Portorož, 2004

today s program
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



Exploratory Network Analysis

with Pajek

(Published at Cambridge University Press, October 2004)

W. de Nooy, A. Mrvar, V. Batagelj


Sunbelt XXIV, Portorož, 2004

Network data

Vertex attributes and properties

Cohesive subgroups:

in simple networks

in signed networks

in valued networks



structural holes

brokerage roles



acyclic networks


Networks and time

repeated measurement


genealogies, citations

Network analysis and statistics

Building your own


Sunbelt XXIV, Portorož, 2004

network data
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

Sunbelt XXIV, Portorož, 2004

vertex attributes and structural properties
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

cohesive subgroups in simple networks
Cohesive subgroupsin simple networks
  • Connectivity
  • Example: Attiro.paj
  • Measures:
    • Components: weak and strong
    • k-cores
    • Cliques,complete subnetworks
  • Analytic strategy

Sunbelt XXIV, Portorož, 2004

cohesive subgroups in signed networks
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

cohesive subgroups in valued networks
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

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

Sunbelt XXIV, Portorož, 2004

  • 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

5 brokerage roles
5 Brokerage roles

Sunbelt XXIV, Portorož, 2004

  • 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

ranks acyclic networks
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

balance theoretic models
Balance-theoretic models

Sunbelt XXIV, Portorož, 2004

triad types and models
Triad types and models

Sunbelt XXIV, Portorož, 2004

  • 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

cohesive subgroups
Cohesive subgroups

Sunbelt XXIV, Portorož, 2004

image matrix
Image matrix

Sunbelt XXIV, Portorož, 2004

blockmodel types
Blockmodel types

Sunbelt XXIV, Portorož, 2004

regular equivalence and errors
Regular equivalence and errors

Sunbelt XXIV, Portorož, 2004

networks and time
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

  • Data format: GEDCOM 5.5 standard
  • Software:- Genealogical Information Manager www.mind home.html- Personal Ancestral File

Sunbelt XXIV, Portorož, 2004

networks and statistics
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

building your own
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

relations among chapters
Relations among chapters

Sunbelt XXIV, Portorož, 2004