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Generalized Binary Blockmodeling
Generalized blockmodeling of binary networks (also relational blockmodeling) is an approach of generalized blockmodeling, analysing the binary network(s). As most network analyses deal with binary networks, this approach is also considered as the fundamental approach of blockmodeling. This is especially noted, as the set of ideal blocks, when used for interpretation of blockmodels, have binary link patterns, which precludes them to be compared with valued empirical blocks. When analysing the binary networks, the criterion function is measuring block inconsistencies, while also reporting the possible errors. The ideal block in binary blockmodeling has only three types of conditions: "a certain cell must be (at least) 1, a certain cell must be 0 and the f over each row (or column) must be at least 1". It is also used as a basis for developing the generalized blockmodeling of valued networks. References {{reflist See also * homogeneity blockmodeling * binary relation * binary ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Generalized Blockmodeling
In generalized blockmodeling, the blockmodeling is done by "the translation of an equivalence type into a set of permitted block types", which differs from the conventional blockmodeling, which is using the indirect approach. It's a special instance of the direct blockmodeling approach. Miha Matjašič, Marjan Cugmas and Aleš Žiberna, blockmodeling: An R package for generalized blockmodeling, ''Metodološki zvezki'', 17(2), 2020, 49–66. Generalized blockmodeling was introduced in 1994 by Patrick Doreian, Vladimir Batagelj and Anuška Ferligoj. Definition Generalized blockmodeling approach is a direct one, "where the optimal partition(s) is (are) identified based on minimal values of a compatible criterion function defined by the difference between empirical blocks and corresponding ideal blocks". At the same time, the much broader set of block types is introduced (while in conventional blockmodeling only certain types are used). The conventional blockmodeling is inductive d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 a distinctive structure through interconnectivity.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. 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.Anuška Ferligoj: Blockmodeling, http://mrvar.fdv.uni-lj.si/sola/info4/nusa/doc/blockmodeling-2.pdf Using blockmodeling, a network can be analyzed using newly created blockmodels, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Network
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 takes two arguments * Binary relation, a relation involving two elements * Binary-coded decimal, a method for encoding for decimal digits in binary sequences * Finger binary, a system for counting in binary numbers on the fingers of human hands Computing * Binary code, the digital representation of text and data * Bit, or binary digit, the basic unit of information in computers * Binary file, composed of something other than human-readable text ** Executable, a type of binary file that contains machine code for the computer to execute * Binary tree, a computer tree data structure in which each node has at most two children Astronomy * Binary star, a star system with two stars in it * Binary planet, two planetary bodies of compa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Social Network Analysis
Social network analysis (SNA) is the process of investigating social structures through the use of networks and graph theory. It characterizes networked structures in terms of ''nodes'' (individual actors, people, or things within the network) and the ''ties'', ''edges'', or ''links'' (relationships or interactions) that connect them. Examples of social structures commonly visualized through social network analysis include social media networks, memes spread, information circulation, friendship and acquaintance networks, business networks, knowledge networks, difficult working relationships, social networks, collaboration graphs, kinship, disease transmission, and sexual relationships. These networks are often visualized through ''sociograms'' in which nodes are represented as points and ties are represented as lines. These visualizations provide a means of qualitatively assessing networks by varying the visual representation of their nodes and edges to reflect attributes of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 representing each cluster as a vertex, from which vertices for another graph 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. The last, third step, using computer program, the partitioning of units is done, according to the pre- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 "cost" associated with the event. An optimization problem seeks to minimize a loss function. An objective function is either a loss function or its opposite (in specific domains, variously called a reward function, a profit function, a utility function, a fitness function, etc.), in which case it is to be maximized. The loss function could include terms from several levels of the hierarchy. In statistics, typically a loss function is used for parameter estimation, and the event in question is some function of the difference between estimated and true values for an instance of data. The concept, as old as Laplace, was reintroduced in statistics by Abraham Wald in the middle of the 20th century. In the context of economics, for example, this ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 representing each cluster as a vertex, from which vertices for another graph 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. The last, third step, using computer program, the partitioning of units is done, according to the pre- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Generalized Blockmodeling Of Valued Networks
Generalized blockmodeling of valued networks is an approach of the generalized blockmodeling, dealing with valued networks (e.g., non–binary). 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 blockmodels, 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) networks (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 para ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 available. This is due to the fact, that homogeneity blockmodeling emphasizes the similarity of link (tie) strengths within the blocks over the pattern of links. In this approach, tie (link) values (or statistical data computed on them) are assumed to be equal (homogenous) within blocks. This approach to the generalized blockmodeling of valued networks was first proposed by Aleš Žiberna in 2007 with the basic idea, "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. Similar approach to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Relation
In mathematics, a binary relation associates elements of one set, called the ''domain'', with elements of another set, called the ''codomain''. A binary relation over Set (mathematics), sets and is a new set of ordered pairs consisting of elements in and in . It is a generalization of the more widely understood idea of a unary function. It encodes the common concept of relation: an element is ''related'' to an element , if and only if the pair belongs to the set of ordered pairs that defines the ''binary relation''. A binary relation is the most studied special case of an Finitary relation, -ary relation over sets , which is a subset of the Cartesian product X_1 \times \cdots \times X_n. An example of a binary relation is the "divides" relation over the set of prime numbers \mathbb and the set of integers \mathbb, in which each prime is related to each integer that is a Divisibility, multiple of , but not to an integer that is not a multiple of . In this relation, for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Matrix
A logical matrix, binary matrix, relation matrix, Boolean matrix, or (0, 1) matrix is a matrix with entries from the Boolean domain Such a matrix can be used to represent a binary relation between a pair of finite sets. Matrix representation of a relation If ''R'' is a binary relation between the finite indexed sets ''X'' and ''Y'' (so ), then ''R'' can be represented by the logical matrix ''M'' whose row and column indices index the elements of ''X'' and ''Y'', respectively, such that the entries of ''M'' are defined by :M_ = \begin 1 & (x_i, y_j) \in R, \\ 0 & (x_i, y_j) \not\in R. \end In order to designate the row and column numbers of the matrix, the sets ''X'' and ''Y'' are indexed with positive integers: ''i'' ranges from 1 to the cardinality (size) of ''X'', and ''j'' ranges from 1 to the cardinality of ''Y''. See the entry on indexed sets for more detail. Example The binary relation ''R'' on the set is defined so that ''aRb'' holds if and only if ''a'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
