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==Blockmodels==
'''BlockmodelBlockmodels''' (sometimes also '''block modelmodels''') isare definedstructures as a multitude of structures,in which are obtained with:
* identification of all vertices (e.g., units, [[node (computer network)|nodes]]) are assembled within a [[Cluster analysis|cluster]], and at the same time representingwith each cluster identified as a [[Vertex (graph theory)|vertex]],; from whichsuch vertices for anothera [[Graph (discrete mathematics)|graph]] can be constructed;
* combinationcombinations 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.<ref>[[Patrick Doreian]], Positional Analysis and Blockmodeling. ''Encyclopedia of Complexity and Systems Science''. DOI: https://doi.org/10.1007/978-0-387-30440-3_412.</ref>
InComputer principle,programs blockmodeling,can as a process, is composed from three steps. Inpartition 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 (mathematics)|matrix]]. The last, third step, using computer program, the partitioning of units is done,object according to the pre-set conditions and additionally, the final matrix is selected for the gained model. With this, the blockmodel is created.<ref name="Exploratory">{{Cite book |last1=Nooy |first1=Wouter de |last2=Mrvar |first2=Andrej |last3=Batagelj |first3=Vladimir |title=Exploratory Social Network Analysis with Pajek. Revised and Expanded Edition for Updated Software. Third Edition |publisher=Cambridge University Press |date=2018 |isbn=978-1-108-47414-6}}</ref>{{rp|333}} When empirical blocks can be reasonably approximated in terms of ideal blocks, such blockmodelblockmodels can be reduced to a '''blockimage''', which is a representation of the original network, capturing its underlying 'functional anatomy'.<ref>{{cite journal |last1=Nordlund |first1=Carl |date=2019 |title=Direct blockmodeling of valued and binary networks: a dichotomization-free approach |url= |journal=Social Networks |volume= 61|issue= |pages= 128–143|doi=10.1016/j.socnet.2019.10.004|arxiv=1910.10484|s2cid=204838377 }}</ref> Thus, 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.<ref>{{cite journal |last1=Arabie |first1=Phipps |last2=Boorman |first2=Scott A. |last3=Levitt |first3=Paul R. |date=1978 |title=Constructing Blockmodels: How and Why |url= |journal=Journal of Mathematical Psychology |volume=17 |issue= |pages=21–63 |doi=10.2307/270873|jstor=270873 }}</ref>
BlockmodelBlockmodels can be created indirectly or directly, based on the construction of the [[criterion function]]. 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 [[Cluster analysis|clustering]] to the corresponding ideal blocks with perfect relations within each cluster and between clusters according to the considered types of connections ([[Equivalence relation|equivalence]])".<ref>{{cite journal |last1=Batagelj |first1=Vladimir |last2=Mrvar |first2=andrej |last3=Ferligoj |first3=Anuška |last4=Doreian |first4=Patrick |date=2004 |title=Generalized Blockmodeling with Pajek |url= https://www.dlib.si/stream/URN:NBN:SI:doc-IK51U9CM/895b643a-1b1d-468f-8970-096c9004202e/PDF|journal=Metodološki zvezki |volume=1 |issue=2 |pages=455–467 |doi=}}</ref> ▼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.<ref>{{cite journal |last1=Arabie |first1=Phipps |last2=Boorman |first2=Scott A. |last3=Levitt |first3=Paul R. |date=1978 |title=Constructing Blockmodels: How and Why |url= |journal=Journal of Mathematical Psychology |volume=17 |issue= |pages=21–63 |doi=10.2307/270873|jstor=270873 }}</ref>
▲Blockmodel can be created indirectly or directly, based on the construction of the [[criterion function]]. 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 [[Cluster analysis|clustering]] to the corresponding ideal blocks with perfect relations within each cluster and between clusters according to the considered types of connections ([[Equivalence relation|equivalence]])".<ref>{{cite journal |last1=Batagelj |first1=Vladimir |last2=Mrvar |first2=andrej |last3=Ferligoj |first3=Anuška |last4=Doreian |first4=Patrick |date=2004 |title=Generalized Blockmodeling with Pajek |url= https://www.dlib.si/stream/URN:NBN:SI:doc-IK51U9CM/895b643a-1b1d-468f-8970-096c9004202e/PDF|journal=Metodološki zvezki |volume=1 |issue=2 |pages=455–467 |doi=}}</ref>
=== Types ===
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