Blockmodeling: Difference between revisions

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{{Short description|Analytical method for social structure}}

{{Merge from|Blockmodel|discuss=Talk:Blockmodeling#Proposed merge of Blockmodel into Blockmodeling|date=March 2022}}

{{Network Science}}

'''Blockmodeling''' is a set or a coherent [[Conceptual framework|framework]], that is used for analyzing [[social structure]] and also for setting procedure(s) for partitioning (clustering) [[social network]]'s units ([[Node (computer science)|nodes]], [[vertice]]s, [[social actor|actors]]), based on specific patterns, which form a distinctive structure through interconnectivity.<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 {{Webarchive|url=https://web.archive.org/web/20230204160352/https://link.springer.com/referenceworkentry/10.1007/978-0-387-30440-3_412 |date=2023-02-04 }}.</ref><ref name="Examples, 1999, pp. 5–34">[[Patrick Doreian]], An Intuitive Introduction to Blockmodeling with Examples, ''BMS: Bulletin of Sociological Methodology'' / ''Bulletin de Méthodologie Sociologique'', January, 1999, No. 61 (January, 1999), pp. 5–34.</ref> It is primarily used in [[statistics]], [[machine learning]] and [[network science]].

As an [[empirical procedure]], blockmodeling assumes that all the units in a specific network can be grouped together to such extent to which they are equivalent. Regarding equivalency, it can be structural, regular or generalized.<ref name="mrvar.fdv.uni-lj.si">[[Anuška Ferligoj]]: Blockmodeling, http://mrvar.fdv.uni-lj.si/sola/info4/nusa/doc/blockmodeling-2.pdf {{Webarchive|url=https://web.archive.org/web/20210812085918/http://mrvar.fdv.uni-lj.si/sola/info4/nusa/doc/blockmodeling-2.pdf |date=2021-08-12 }}</ref> Using blockmodeling, a [[Social network|network]] can be analyzed using newly created [[blockmodel]]s, which transforms large and complex network into a smaller and more comprehensible one. At the same time, the blockmodeling is used to operationalize [[social role]]s.

While some contend that the blockmodeling is just clustering methods, [[Phillip Bonacich|Bonacich]] and [[Maureen J. McConaghy|McConaghy]] state that "it is a theoretically grounded and algebraic approach to the analysis of the structure of relations". Blockmodeling's unique ability lies in the fact that it considers the structure not just as a set of direct relations, but also takes into account all other possible compound relations that are based on the direct ones.<ref>{{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>

The principles of blockmodeling were first introduced by [[Francois Lorrain]] and [[Harrison C. White]] in 1971.<ref name="Examples, 1999, pp. 5–34"/> Blockmodeling is considered as "an important set of network analytic tools" as it deals with delineation of role structures (the well-defined places in social structures, also known as positions) and the discerning the fundamental structure of social networks.<ref name="gener-black">{{Cite book |last1=Doreian |first1=Patrick |last2=Batagelj |first2=Vladimir |last3=Ferligoj |first3=Anuška |title=Generalized BlackmodelingBlockmodeling |publisher=Cambridge University Press |date=2005 |isbn=0-521-84085-6}}</ref>{{rp|2, 3}} According to [[Vladimir Batagelj|Batagelj]], the primary "goal of blockmodeling is to reduce a large, potentially incoherent network to a smaller comprehensible structure that can be interpreted more readily".<ref>{{cite journal |last1=Batagelj |first1=Vladimir |date=1999 |title=Generalized Blockmodeling |url= |journal=Informatica |volume=23 |issue= |pages=501–506 |doi=}}</ref> Blockmodeling was at first used for analysis in [[sociometry]] and [[psychometrics]], but has now spread also to other sciences.<ref>[{{Cite web |url=https://www.iioa.org/conferences/16th/files/Papers/Weber%20Introducing%20blockmodeling%20to%20input-output%20analysis.doc |title=WEBER, M. (2007), “Introducing blockmodeling to input-output analysis”. 16th International I-Ot Conf, Istanbul, Turkey.] |access-date=2021-08-23 |archive-date=2021-08-23 |archive-url=https://web.archive.org/web/20210823084150/https://www.iioa.org/conferences/16th/files/Papers/Weber%20Introducing%20blockmodeling%20to%20input-output%20analysis.doc |url-status=live }}</ref>

== Definition ==

[[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 beingundergoing blockmodeledblockmodeling, 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 multilevelandmultilevel 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"/>

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Among direct blockmodeling approaches are: [[structural equivalence]] and [[regular equivalence]].<ref name="Examples, 1999, pp. 5–34"/> Structural equivalence is a state, when units are connected to the rest of the network in an identical way(s), while regular equivalence occurs when units are equally related to equivalent others (units are not necessarily sharing neighbors, but have neighbour that are themselves similar).<ref name="mrvar.fdv.uni-lj.si"/><ref name="gener-black"/>{{rp|24}}

[[File:Regular equivalence.jpg|thumb|Regular equivalence]]

Indirect blockmodeling approaches, where partitioning is dealt with as a traditional cluster analysis problem (measuring (dis)[[Similarity (network science)|similartysimilarity]] results in a (dis)similartiysimilarity matrix), are:<ref name="ReferenceA"/><ref name="Examples, 1999, pp. 5–34"/>

* [[conventional blockmodeling]],

* [[generalized blockmodeling]]:

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* [[exploratory blockmodeling|exploratory]] or [[confirmatory blockmodeling]].

==Blockmodels==

== Creation of a blockmodel ==

'''Blockmodels''' (sometimes also '''block models''') are structures in which:

{{mainarticle|Blockmodel}}

* vertices (e.g., units, [[node (computer network)|nodes]]) are assembled within a [[Cluster analysis|cluster]], with each cluster identified as a [[Vertex (graph theory)|vertex]]; from such vertices a [[Graph (discrete mathematics)|graph]] can be constructed;

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. 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.<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}}

* combinations 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 {{Webarchive|url=https://web.archive.org/web/20230204160352/https://link.springer.com/referenceworkentry/10.1007/978-0-387-30440-3_412 |date=2023-02-04 }}.</ref>

Computer programs can partition the social network according to pre-set conditions.<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 blockmodels 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>

Blockmodels 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= |access-date=2023-01-07 |archive-date=2022-03-22 |archive-url=https://web.archive.org/web/20220322081928/http://www.dlib.si/stream/URN:NBN:SI:DOC-IK51U9CM/895b643a-1b1d-468f-8970-096c9004202e/PDF |url-status=live }}</ref>

=== Types ===

Blockmodels can be specified regarding the [[intuition]], [[wikt:substance|substance]] or the insight into the nature of the studied network; this can result in such models as follows:<ref name="gener-black"/>{{rp|16-24}}

* [[parent-child role]] systems,

* [[organizational hierarchy|organizational hierarchies]],

* systems of [[ranked cluster]]s,...

== Specialized programs ==

Blockmodeling is done with specialized [[computer program]]s, dedicated to the analysis of networks or blockmodeling in particular, as:

* '''BLOCKS''' ([[Tom Snijders]]),<ref name="stats.ox.ac.uk">[https://www.stats.ox.ac.uk/~snijders/socnet.htm STATS.ox.ac.uk – Social Network Analysis]</ref>

* '''[[CONCOR]]''',<ref>{{cite journal |last1=Steiber |first1=Steven R. |date=1981 |title=Building better blockmodels: A non–hierarchical extension of CONCOR with applications to regression analysis |url= |journal=Mid–American Review of Sociology |volume=VI |issue= |pages=17–40 |doi=}}</ref>

* '''Model''' ([[Vladimir Batagelj]]),<ref name="Generalized Blockmodeling with Paje">{{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= |journal=Metodološki zvezki |volume=1 |issue=2 |pages=455–467 |doi=}}</ref>

* '''Model2''' (Vladimir Batagelj),<ref name="Generalized Blockmodeling with Paje"/>

* '''[[Pajek]]''' (Vladimir Batagelj and [[Andrej Mrvar]]),<ref name="Generalized Blockmodeling with Paje"/>

* '''[[R (programming language)|R]]–package Blockmodeling''' ([[Aleš Žiberna]]),<ref name="Absent Ties in Social Networks, the"/><ref>[httpshttp://cran.r–projectr-project.org/web/packages/blockmodeling/blockmodeling.pdf Cran.R–project.org – Package 'blockmodeling']</ref><ref name="ReferenceA"/>

* '''Socnet.se''': The blockmodeling console app (Win/Linux/Mac) (Carl Nordlund)<ref>{{Cite web |last=Nordlund |first=Carl |date=2024 |title=Socnet.se: The blockmodeling console app |url=https://socnet.se/ |access-date=2025-06-04 |website=socnet.se |language=en}}</ref>

* '''StOCNET''' (Tom Snijders),...<ref name="stats.ox.ac.uk" />

** '''BLOCKS''' ([[Tom Snijders]]),<ref name="stats.ox.ac.uk">[{{Cite web |url=https://www.stats.ox.ac.uk/~snijders/socnet.htm |title=STATS.ox.ac.uk – Social Network Analysis] |access-date=2021-08-18 |archive-date=2021-08-18 |archive-url=https://web.archive.org/web/20210818092755/https://www.stats.ox.ac.uk/~snijders/socnet.htm |url-status=live }}</ref>

* '''[[CONCOR]]''',<ref>{{cite journal |last1=Steiber |first1=Steven R. |date=1981 |title=Building better blockmodels: A non–hierarchical extension of CONCOR with applications to regression analysis |url= |journal=Mid–American Review of Sociology |volume=VI |issue= |pages=17–40 |doi=}}</ref>

* '''Model''' and '''Model2''' ([[Vladimir Batagelj]]),<ref name="Generalized Blockmodeling with Paje">{{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= |journal=Metodološki zvezki |volume=1 |issue=2 |pages=455–467 |doi=}}</ref>

== See also ==

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* [[Mathematical sociology]]

* [[Role assignment]]

* [[multiobjectiveMultiobjective blockmodeling]]

* [[blockmodelingBlockmodeling linked networks]]

== References ==

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{{Social networking}}

[[Category:Machine learning]]

[[Category:Network science]]

[[Category:Blockmodeling| ]]