Blockmodeling: Difference between revisions

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Blockmodeling can thus be defined as a set of approaches for partitioning units into clusters (also known as positions) and links into blocks, which are further defined by the newly obtained clusters. A block (also blockmodel) is defined as a submatrix, that shows interconnectivity (links) between nodes, present in the same or different clusters.<ref name="ReferenceA"/> Each of these positions in the cluster is defined by a set of (in)direct ties to and from other social positions.<ref name="The Algebra of Blockmodeling">{{cite journal |last1=Bonacich |first1=Phillip |last2=McConaghy |first2=Maureen J. |date=1980 |title=The Algebra of Blockmodeling |url= |journal=Sociological Methodology |volume=11 |issue= |pages=489–532 |doi=10.2307/270873}}</ref>

[[Matrix]] (which can also be shown as a graph) is composed of ordered units, in rows and columns, based on their names. Such ordered units are then divided (partitioned) based on the similarity: units with similar patterns of links are partitioned together in the same clusters. Clusters are then arranged together so that units from the same clusters are placed next to each other and thus preserving the interconnectivity. In the next step, the units (from the same clusters) are transformed into a blockmodel. With this, several blockmodels are usually formed, one being core cluster and others being cohesive; core cluster is always connected to cohesive ones, while cohesive ones can not be linked together. Clustering of nodes is based on the [[Equivalence relation|equivalence]]{{dn|date=August 2021}}, such as structural and regular.<ref name="ReferenceA"/> Primary objective of the matrix form is visually present relations between the persons included in the cluster. These ties are coded dichotomously (as present or absent), and the rows in the matrix form indicate the source of the ties, while the columns represent the destination of said ties.<ref name="The Algebra of Blockmodeling"/>

Equivalence can have two basic approaches: the equivalent units have the same connection pattern to the same neighbors or these units have same or similar connection pattern to different neighbors. If the units are connected to the rest of network in identical ways, then they are structurally equivalent.<ref name="mrvar.fdv.uni-lj.si"/> Units can also be regularly equivalent, when they are equivalently connected to equivalent others.<ref name="Examples, 1999, pp. 5–34"/>