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Top1. Introduction
The discovery of social structure in the network of actors with multiple relations is called positional analysis. During positional analysis process, blockmodeling as a way of simplifying, size reducing and making the structure of each social network be comprehensible, consists of two major, essential components: partitioning of actors to positions (or equivalent classes) and clarifying relations between and within positions. Multiple definitions have been proposed by authors for equivalent classes. Pioneer of them is structural equivalence (SE), introduced by Lorrain and White (1971), which implies that two actors belong to the same structural equivalent class iff they have identical ties to / from all other actors. The other definitions are automorphic, isomorphic and regular equivalence. As mentioned by (Wasserman & Faust, 1994), the definition of equivalence by SE has more adherents among researchers for positional analysis of social networks. In order to reveal the social structure of each network, the relations between and within positions must be specified and this can be done by density matrices, image matrices and reduced graphs. In fact at the end of each positional analysis, the social structure of each network can be summarized in the form of image/density matrices or reduced graphs. With the above considerations, each blockmodel has at least: a partition vector indicating the partitioning of actors to positions and a set of image matrices showing the social structure of each network.
The determination sequence of two components of the blockmodel help distinguish between generalized and conventional blockmodeling so that while actor partitioning in conventional blockmodeling is performed by clustering on distances of actors from each other based on several equivalence definitions, such as structural and regular equivalence, generalized blockmodeling procedure of Doreian, Batagelj, and Ferligoj (2005), using a local optimization procedure, searches the best partition vector that best satisfies a predetermined social structure. In fact, in generalized blockmodeling, actor partitioning is done without need to any equivalence definition, by local searching for the best partition vector agree with the predefined social structure. This generalization of blockmodeling could be adopted for two-mode network by Doreian, Batagelj, and Ferligoj (2004), signed network by Doreian and Mrvar (2009), sparse network by Žiberna (2013), multilevel network by Žiberna (2014), and valued networks by Žiberna (2007), which were implemented in Pajek software and blockmodeling R package. However if the predefined social structure is unknown, the applicability and feasibility of generalized blockmodeling would be limited.