### Blockmodeling - structural and regular equivalence

1. Introduction to blockmodeling
2. Equivalences
• Structural equivelence
• Regular equivelence
• Generalized blockmodeling
3. Determining blockmodels
• Indirect approach
• Direct approach
4. Examples

### Community detection methods

1. Louvain method
2. VOS clustering
3. Examples
4. More on community detection

Examples

1. For Sampson monastery network
• draw dendrogram of monks with indirect approach according to structural equivalence
• compute blockmodel with direct approach according to structural equivalence in the number of groups that is shown in dendrogram
• compute blockmodel with direct approach according to regular equivalence in two groups
2. Find communities in given networks.

First Assignment

• draw dendrogram with indirect approach according to structural equivalence
• compute blockmodel with direct approach according to structural equivalence:
• optimize solution obtained by the indirect approach
• find solution with random start
• compute blockmodel with direct approach according to regular equivalence into 2, 3, and 4 groups
• Interprete results.

Second Assignment

1. Check if your network is compatible with the following models:
• cohesive groups (clustering)
• core-periphery
• general model which you define by your own
Which model fits your data the best (take into account also structural and regular equivalence)? Interprete each of the models.
2. Find communities using Louvain method and VOS Clustering (resolution parameter r=1). Compute Cramer and other coefficients to compare partitions obtained by both methods. According to result, find communities also with another value of resolution parameter (larger or smaller than 1). Interprete all results.

Slides (PDF)
Figure: Generalized equivalence / block types (PDF)
Generalized Blockmodeling with Pajek (paper which uses class1.net)
Test data (ZIP)
Blockmodeling in Pajek (PDF)
Community Detection in Pajek (PDF)