Blockmodeling: Difference between revisions

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[[File:Social network characteristics diagram.jpg|thumb|upright=1.5|left|350px|Different characteristics of social networks. A, B, and C show varying centrality and density of networks; panel D shows network closure, i.e., when two actors, tied to a common third actor, tend to also form a direct tie between them. Panel E represents two actors with different attributes (e.g., organizational affiliation, beliefs, gender, education) who tend to form ties. Panel F consists of two types of ties: friendship (solid line) and dislike (dashed line). In this case, two actors being friends both dislike a common third (or, similarly, two actors that dislike a common third tend to be friends).]]

NetworkA network as a system is composed of (or defined) by) two different sets: one set of units (nodes, vertices, actors) and one set of links between the units. Using both sets, it is possible to create a [[graph (discrete mathematics)|graph]], describing the structure of the network.<ref name="ReferenceA">[[Miha Matjašič]], [[Marjan Cugmas]] and [[Aleš Žiberna]], blockmodeling: An R package for generalized blockmodeling, ''Metodološki zvezki'', 17(2), 2020, 49–66.</ref>

During blockmodeling, the researcher is faced with two problems: how to partition the units (e.g., how to determine the [[Cluster analysis|clusters]] (or classes), that then form vertices in a blockmodel) and then how to determine the links in the blockmodel (and at the same time the values of these links).<ref>{{cite journal |last1=Batagelj |first1=Vladimir |date=1997 |title=Notes on blockmodeling |url= |journal=Social Networks |volume=19 |issue= |pages=143–155}}</ref>

WhenIn analyzing a [[social network]] (inthe [[social sciences]]), the networks are usually [[social network]]s, composed of several individuals (units) and selected [[social relationship]]s among them (links). As such realReal-world networks can be large and complex, a; blockmodeling is used to simplify them into smaller structures, that can be much easier to interpret. Specifically, blockmodeling partitions the units into clusters and then determines the ties among the said clusters. At the same time, blockmodeling can be used to explain the [[social role]]s, existing in suchthe network, as it is assumed that the created cluster of units mimics (or is closely associated) with) the units' social roles.<ref name="ReferenceA"/>

[[File:6n-graf.svg|thumb|250px|right|In [[graph theory]], the image provides a simplified view of a network, where each of the numbers represents a different node.]]

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> These links (connections) can be directed or undirected; there can be multiple links between the same pair of objects or they can have weights on them. If there are not any multiple links in a network, it is called a simple network.<ref>Brian Joseph Ball, ''Blockmodeling techniques for complex networks: doctoral dissertation.'' University of Michigan, 2014.</ref>{{rp|8}}

A [[Matrix (mathematics)|Matrixmatrix]] (whichrepresentation can also be shown asof a graph) is composed of ordered units, in rows and columns, based on their names. SuchThe 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; a core cluster is always connected to cohesive ones, while cohesive ones can notcannot be linked together. Clustering of nodes is based on the [[Equivalence relation|equivalence]], such as structural and regular.<ref name="ReferenceA"/> PrimaryThe primary objective of the matrix form is to 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 saidthe 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"/>

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== Different approaches ==

Regarding what kind of network is undergoing blockmodeling, a different approach is necessary. Networks can be one–mode or two–mode. In the former all units can be connected to any other unit and where units are of the same type, while in the latter the units are connected only to the unit(s) of a different type.<ref name="gener-black"/>{{rp|6–10}} Regarding relationships between units, they can be single–relational or multi–relational networks. Further more, the networks can be temporal or multilevel and also binary (only 0 and 1) or signed (allowing negative ties)/values (other values are possible) networks.

Different approaches to blockmodeling can be grouped into two main classes: [[deterministic blockmodeling]] and [[stochastic blockmodeling]] approaches. Deterministic blockmodeling is then further divided into direct and indirect blockmodeling approaches.<ref name="ReferenceA"/>