Blockmodel (sometimes also block model) in

blockmodeling Blockmodeling is a set or a coherent framework, that is used for analyzing social structure and also for setting procedure(s) for partitioning (clustering) social network's units ( nodes, vertices, actors), based on specific patterns, which form ...

(part of

network science Network science is an academic field which studies complex networks such as telecommunication networks, computer networks, biological networks, cognitive and semantic networks, and social networks, considering distinct elements or actors repr ...

) is defined as a multitude of structures, which are obtained with: * identification of all vertices (e.g., units,

nodes In general, a node is a localized swelling (a "knot") or a point of intersection (a vertex). Node may refer to: In mathematics *Vertex (graph theory), a vertex in a mathematical graph *Vertex (geometry), a point where two or more curves, lines, ...

) within a

cluster may refer to: Science and technology Astronomy * Cluster (spacecraft), constellation of four European Space Agency spacecraft * Asteroid cluster, a small asteroid family * Cluster II (spacecraft), a European Space Agency mission to study th ...

and at the same time representing each cluster as a

vertex Vertex, vertices or vertexes may refer to: Science and technology Mathematics and computer science *Vertex (geometry), a point where two or more curves, lines, or edges meet *Vertex (computer graphics), a data structure that describes the position ...

, from which vertices for another

graph Graph may refer to: Mathematics *Graph (discrete mathematics), a structure made of vertices and edges **Graph theory, the study of such graphs and their properties *Graph (topology), a topological space resembling a graph in the sense of discre ...

can be constructed; * combination of all the links (ties), represented in a block as a single link between positions, while at the same time constructing one tie for each block. In a case, when there are no ties in a block, there will be no ties between the two positions, that define the block. In principle, blockmodeling, as a process, is composed from three steps. In the first step, the number of units is determined. This is followed (in the second step) by selection or determination of permitted blocks, that will occur and perhaps also the locations in the

matrix Matrix most commonly refers to: * ''The Matrix'' (franchise), an American media franchise ** '' The Matrix'', a 1999 science-fiction action film ** "The Matrix", a fictional setting, a virtual reality environment, within ''The Matrix'' (franchi ...

. The last, third step, using computer program, the partitioning of units is done, according to the pre-set conditions and additionally, the final matrix is selected for the gained model. With this, the blockmodel is created. When empirical blocks can be reasonably approximated in terms of ideal blocks, such blockmodel can be reduced to a blockimage, which is a representation of the original network, capturing its underlying 'functional anatomy'. Thus, the blockmodels can "permit the data to characterize their own structure", and at the same time not seek to manifest a preconceived structure imposed by the researcher. Blockmodel can be created indirectly or directly, based on the construction of the

criterion function In mathematical optimization and decision theory, a loss function or cost function (sometimes also called an error function) is a function that maps an event or values of one or more variables onto a real number intuitively representing some "cos ...

. Indirect construction refers to a function, based on "compatible (dis)similarity measure between paris of units", while the direct construction is "a function measuring the fit of real blocks induced by a given clustering to the corresponding ideal blocks with perfect relations within each cluster and between clusters according to the considered types of connections ( equivalence)".

Specification of blockmodels

Blockmodels can be specified regarding the

intuition Intuition is the ability to acquire knowledge without recourse to conscious reasoning. Different fields use the word "intuition" in very different ways, including but not limited to: direct access to unconscious knowledge; unconscious cognition; ...

substance Substance may refer to: * Matter, anything that has mass and takes up space Chemistry * Chemical substance, a material with a definite chemical composition * Drug substance ** Substance abuse, drug-related healthcare and social policy diagnosis o ...

or the insight into the nature of the studied network; this can result in such models as follows: * parent-child role systems, * organizational hierarchies, * systems of

ranked cluster A ranking is a relationship between a set of items such that, for any two items, the first is either "ranked higher than", "ranked lower than" or "ranked equal to" the second. In mathematics, this is known as a weak order or total preorder of o ...

s, *

baboon grooming network Baboons are primates comprising the genus ''Papio'', one of the 23 genera of Old World monkeys. There are six species of baboon: the hamadryas baboon, the Guinea baboon, the olive baboon, the yellow baboon, the Kinda baboon and the cha ...

s, ...

References

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Specification of blockmodels

References

See also