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Abstract
One goal of blockmodeling is to reduce a large, potentially incoherent network to a smaller comprehensible structure that can be interpreted more readily. Batagelj, Doreian, and Ferligoj developed a generalized approach to blockmodeling and methods where a set of observed relations are fitted to a pre-specified blockmodel. In the paper this generalized blockmodeling approach as implemented in program Pajek is described. An overview of the blockmodeling procedures in Pajek is given and is illustrated by some examples.
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1 Introduction
Blockmodeling has been a main focus of network analysts (Hummon and Carley, 1993) with position as a central concept (Borgatti and Everett, 1992). Blockmodeling seeks to cluster units which have substantially similar patterns of relationships with others, and interpret the pattern of relationships among clusters.
Pajek is a program designed for the analysis of large networks (Batagelj and Mrvar, 1998, 2002, 2003, 2004). Initially generalized blockmodeling, as developed by Batagelj, Doreian, and Ferligoj, was supported by two programs Model and Model2 (Batagelj, 1996). To provide additional support for analysis of smaller parts of large networks the authors of Pajek - Batagelj and Mrvar - decided to include also some procedures for generalized blockmodeling into Pajek. These procedures are time consuming and therefore can be applied only to the networks of moderate size (up to some hundreds).
The aim of the paper is to provide an overview of the blockmodeling procedures implemented in Pajek together with some examples. The basic blockmodeling procedures in Pajek are described in detail in the monograph Exploratory Network Analysis with Pajek (de Nooy, Mrvar, and Batagelj, 2004). An extended discussion of generalized blockmodeling can be found in the monograph Generalized Block- modeling (Doreian, Batagelj, and Ferligoj, 2004). Here, only the main ideas and procedures for generalized blockmodeling are given and the basic knowledge of how to use Pajek is assumed.
2 Basic definitions
Let us start with some basic definitions.
Let U = {X1,X2, . . . ,Xn} be a finite set of units. The units are related by a binary relation
...
which determine a network
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The relation R can be also described by a corresponding binary matrix R = ...
where
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In some applications rij can be a nonnegative real...