Journal•ISSN: 0022-250X
Journal of Mathematical Sociology
Taylor & Francis
About: Journal of Mathematical Sociology is an academic journal published by Taylor & Francis. The journal publishes majorly in the area(s): Population & Social network. It has an ISSN identifier of 0022-250X. Over the lifetime, 695 publications have been published receiving 35011 citations.
Topics: Population, Social network, Mathematical sociology, Dynamic network analysis, Stochastic modelling
Papers published on a yearly basis
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TL;DR: The systemic effects are found to be overwhelming: there is no simple correspondence of individual incentive to collective results, and a general theory of ‘tipping’ begins to emerge.
Abstract: Some segregation results from the practices of organizations, some from specialized communication systems, some from correlation with a variable that is non‐random; and some results from the interplay of individual choices. This is an abstract study of the interactive dynamics of discriminatory individual choices. One model is a simulation in which individual members of two recognizable groups distribute themselves in neighborhoods defined by reference to their own locations. A second model is analytic and deals with compartmented space. A final section applies the analytics to ‘neighborhood tipping.’ The systemic effects are found to be overwhelming: there is no simple correspondence of individual incentive to collective results. Exaggerated separation and patterning result from the dynamics of movement. Inferences about individual motives can usually not be drawn from aggregate patterns. Some unexpected phenomena, like density and vacancy, are generated. A general theory of ‘tipping’ begins to emerge.
4,238 citations
TL;DR: New algorithms for betweenness are introduced in this paper and require O(n + m) space and run in O(nm) and O( nm + n2 log n) time on unweighted and weighted networks, respectively, where m is the number of links.
Abstract: Motivated by the fast‐growing need to compute centrality indices on large, yet very sparse, networks, new algorithms for betweenness are introduced in this paper. They require O(n + m) space and run in O(nm) and O(nm + n2 log n) time on unweighted and weighted networks, respectively, where m is the number of links. Experimental evidence is provided that this substantially increases the range of networks for which centrality analysis is feasible. The betweenness centrality index is essential in the analysis of social networks, but costly to compute. Currently, the fastest known algorithms require ?(n 3) time and ?(n 2) space, where n is the number of actors in the network.
4,190 citations
TL;DR: In this paper, Factoring and weighting approaches to status scores and clique identification were proposed, and the results showed that the weighting approach is more accurate than the factoring approach.
Abstract: (1972). Factoring and weighting approaches to status scores and clique identification. The Journal of Mathematical Sociology: Vol. 2, No. 1, pp. 113-120.
2,661 citations
TL;DR: In this article, an extension of the dichotomous probit model for ordinal dependent variables is presented. But the model assumes that the ordinal nature of the observed dependent variable is due to methodological limitations in collecting the data, which force the researcher to lump together and identify various portions of an interval level variable.
Abstract: This paper develops a model, with assumptions similar to those of the linear model, for use when the observed dependent variable is ordinal. This model is an extension of the dichotomous probit model, and assumes that the ordinal nature of the observed dependent variable is due to methodological limitations in collecting the data, which force the researcher to lump together and identify various portions of an (otherwise) interval level variable. The model assumes a linear eflect of each independent variable as well as a series of break points between categories for the dependent variable. Maximum likelihood estimators are found for these parameters, along with their asymptotic sampling distributions, and an analogue of R 2 (the coefficient of determination in regression analysis) is defined to measure goodness of fit. The use of the model is illustrated with an analysis of Congressional voting on the 1965 Medicare Bill.
2,520 citations
TL;DR: In this article, the authors derive global patterns of global relations from a detailed social network, within which classes of equivalently positioned individuals are delineated by a "functorial" mapping of the original pattern.
Abstract: The aim of this paper is to understand the interrelations among relations within concrete social groups. Social structure is sought, not ideal types, although the latter are relevant to interrelations among relations. From a detailed social network, patterns of global relations can be extracted, within which classes of equivalently positioned individuals are delineated. The global patterns are derived algebraically through a ‘functorial’ mapping of the original pattern. Such a mapping (essentially a generalized homomorphism) allows systematically for concatenation of effects through the network. The notion of functorial mapping is of central importance in the ‘theory of categories,’ a branch of modern algebra with numerous applications to algebra, topology, logic. The paper contains analyses of two social networks, exemplifying this approach.
1,488 citations