Generalized blockmodeling of valued networks is an approach of the generalized

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 ...

, dealing with

valued network Value or values may refer to: Ethics and social * Value (ethics) wherein said concept may be construed as treating actions themselves as abstract objects, associating value to them ** Values (Western philosophy) expands the notion of value beyo ...

s (e.g., non–

binary Binary may refer to: Science and technology Mathematics * Binary number, a representation of numbers using only two digits (0 and 1) * Binary function, a function that takes two arguments * Binary operation, a mathematical operation that ta ...

). While the generalized blockmodeling signifies a "formal and integrated approach for the study of the underlying functional anatomies of virtually any set of relational data", it is in principle used for binary networks. This is evident from the set of ideal blocks, which are used to interpret

blockmodel Blockmodel (sometimes also block model) in blockmodeling (part of network science) is defined as a multitude of structures, which are obtained with: * identification of all vertices (e.g., units, nodes) within a cluster and at the same time repre ...

s, that are binary, based on the characteristic link patterns. Because of this, such templates are "not readily comparable with valued empirical blocks". To allow generalized blockmodeling of valued directional ( one–mode)

network Network, networking and networked may refer to: Science and technology * Network theory, the study of graphs as a representation of relations between discrete objects * Network science, an academic field that studies complex networks Mathematics ...

s (e.g. allowing the direct comparisons of empirical valued blocks with ideal binary blocks), a non–parametric approach is used. With this, "an optional parameter determines the prominence of valued ties as a minimum percentile deviation between observed and expected flows". Such two–sided application of parameter then introduces "the possibility of non–determined ties, i.e. valued relations that are deemed neither prominent (1) nor non–prominent (0)." Resulted occurrences of links then motivate the modification of the calculation of inconsistencies between empirical and ideal blocks. At the same time, such links also give a possibility to measure the interpretational certainty, which is specific to each ideal block. Such maximum two–sided deviation threshold, holding the aggregate uncertainty score at zero or near–zero levels, is then proposed as "a measure of interpretational certainty for valued blockmodels, in effect transforming the optional parameter into an outgoing state". Problem with blockmodeling is the standard set of ideal block, as they are all specified using binary link (tie) patters; this results in "a non–trivial exercise to match and count inconsistencies between such ideal binary ties and empirical valued ties". One approach to solve this is by using

dichotomization In applied mathematics, discretization is the process of transferring continuous functions, models, variables, and equations into discrete counterparts. This process is usually carried out as a first step toward making them suitable for numeric ...

to transform the network into a binary version. The other two approaches were first proposed by

Aleš Žiberna Aleš Žiberna is a Slovene statistician, whose specialty is network analysis. His specific research interests include blockmodeling, multivariate analysis and computer intensive methods (e.g., computer simulations, resampling methods). Curr ...

2007 File:2007 Events Collage.png, From top left, clockwise: Steve Jobs unveils Apple's first iPhone; TAM Airlines Flight 3054 overruns a runway and crashes into a gas station, killing almost 200 people; Former Pakistani Prime Minister Benazir Bhutto ...

by introducing valued (generalized) blockmodeling and also

homogeneity blockmodeling In mathematics applied to analysis of social structures, homogeneity blockmodeling is an approach in blockmodeling, which is best suited for a preliminary or main approach to valued networks, when a prior knowledge about these networks is not avai ...

. The basic idea of the latter is "that the inconsistency of an empirical block with its ideal block can be measured by within block variability of appropriate values". The newly–formed ideal blocks, which are appropriate for blockmodeling of valued networks, are then presented together with the definitions of their block inconsistencies. Two other approaches were later suggested by

Carl Nordlund Carl may refer to: *Carl, Georgia, city in USA *Carl, West Virginia, an unincorporated community * Carl (name), includes info about the name, variations of the name, and a list of people with the name *Carl², a TV series * "Carl", an episode of te ...

in 2019: deviational approach and correlation-based generalized approach. Both Nordlund's approaches are based on the idea, that valued networks can be compared with the ideal block without values. With this approach, more information is retained for analysis, which also means, that there are fewer partitions having identical values 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 ...

. This means, that the generalized blockmodeling of valued networks measures the inconsistencies more precisely. Usually, only one optimal partition is found in this approach, especially when it is used by homogeneity blockmodeling. Contrary, while using binary blockmodeling on the same sample, usually more than one optimal partition had occurred on several occasions.

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See also