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In this paper we examine some of the mathematical properties of Everett's graph theoretic blocking procedures. In particular we discuss how k-plexes are blocked by Everett's algorithm. We also give a mathematical definition and algorithm f or finding a class of actors identified as important in Everett's paper. [ABSTRACT FROM AUTHOR]

The Harary-Ross clique detection algorithm has often been neglected in analyses of symmetric graphs and tolerance relations because of presumed storage and computation problems. This paper presents a modification of the original algorithm which overcomes these difficulties. The modified algorithm is shown to perform as well as other recent structurally different algorithms. Indeed, for arc densities which might be expected in typical sociometric analyses, the modified algorithm has certain conceptual and operational advantages. The paper also indicates possible applications of the algorithm in the analysis of non-symmetric functional relations and points out the conceptual similarity with simplicial connectivity analysis. [ABSTRACT FROM AUTHOR]

This paper discusses two algorithms that compute important structural properties of dynamic social networks. The properties are hierarchy in a directed graph, and balance at a node in a signed directed graph. The hierarchy algorithm is used in a model that generates dominance structures in groups. The balance algorithm is part of a model that generates deviant behavior in a group. Both algorithms work with dynamic network data structure that changes with each social event of the theoretical simulation model. These changes include: adding and deleting nodes; and adding, deleting, and changing the value of ties. To be useful, these algorithms must be efficient became hierarchy and balance occurs continuously the running of the simulation models. [ABSTRACT FROM AUTHOR]

The article discusses a stability proof for an interactive Markov chain. An interactive Markov chain is one in which the transition probabilities applying to each individual of a population are functions of the frequencies by state of the rest of the population. This functional dependence allows social interaction among individuals, whereas conventional Markov chains assume away such interaction. Let P = [Pij] be the KXK transition matrix applying to each individual; where Pij is the probability of transition from state j to state i. The elements of P must be nonnegative, and all column sums must equal one. Throughout, when the symbols ≥ and > are used with an array, they will mean every element greater than or equal to and every element greater than, respectively. It is known from the theory of nonnegative matrices that A has a dominant eigenvalue which is real, positive and of multiplicity one. This dominant eigenvalue has a corresponding dominant eigenvector which has all elements positive and which is unique up to a scalar multiple. To put the primitivity assumption in perspective, it is useful to recall that, in the ordinary Markov chain case b = 0, primitivity is both necessary and sufficient for convergence.

Researchers have identified several problems in measuring the strongest path connecting pairs of actors in valued graphs. To address these problems, it has been proposed that average path value be used to indicate optimal connections between dyads. However, a lack of proper computer algorithm and its implementation has hindered a wide-range application of the proposed solution. In this paper we develop a computer algorithm and fully implement it with four JAVA programs, which are available on request. These programs produce an optimal connection matrix, which is subsequently inputted into UCINET for further multidimensional scaling and clustering analysis. We demonstrate this procedure with a data matrix containing 38 organizations in information technology. We discuss the methodological implications of the application of our algorithm to future social network studies. [ABSTRACT FROM AUTHOR]

In this paper, two different views of sociality, one based upon interferences, and the other based upon complementarity, or interdependence, arc confronted. The latter is shown to present a number of theoretical advantages over the former, allowing for an account of different types of social actions--influencing, exchange, cooperation--and of how these emerge from structural social conditions. A formal model of dependence relations is presented, and an algorithm for calculating the dependence networks and situations in a multi-agent context is briefly shown. A simulator of dependence relations, which edits a set of agents (in terms of their goals, actions, and plans) and applies the algorithm to calculate their dependence relations relative to any given goal, is described, and its applications are discussed. Some elementary simulations are exemplified in order to illustrate the experimental application of the simulator in a two-agent context. Future expansions of the simulator are finally discussed. [ABSTRACT FROM AUTHOR]

Configurational comparative methods have gained in popularity among sociologists and political scientists. In particular, Qualitative Comparative Analysis (QCA) has attracted considerable attention in recent years. The process of Boolean minimization by means of the Quine-McCluskey algorithm (QMC) is the central procedure in QCA, but QMC's exactitude renders it memory intensive and slow in processing complex output functions. In this article, we introduce the enhanced QMC algorithm (eQMC) to alleviate these problems. eQMC is equally exact but, unlike QMC, capable of processing multivalent condition and outcome factors. Instead of replacing QMC, however, eQMC acts as an optimizing complement in contexts of limited empirical diversity. We demonstrate its speed and computer memory performance through simulations. [ABSTRACT FROM AUTHOR]

Marengo and Settepanella (2010) have developed a geometric model of social choice when it takes place among bundles of interdependent elements, showing that by bundling and unbundling the same set of constituent elements an authority has the power of determining the social outcome. In this article, we will tie the model above to tournament theory, solving some of the mathematical problems arising in their work and opening new questions which are interesting from both a mathematical and social choice point of view. In particular, we will introduce the notion of u-local optima and study it from both a theoretical and a numerically probabilistic point of view; we will also describe an algorithm that computes the universal basin of attraction of a social outcome in O(M 3log M) time (where M is the number of social outcomes). [ABSTRACT FROM AUTHOR]

The aim of this article is to compare methods for detecting and/or measuring regular equivalence in valued networks. The methods compared can be divided into direct and indirect methods. The indirect methods considered here are all variants of the REGE algorithm (White, 2005). All direct methods have roots in Batagelj, Doreian, and Ferligoj (1992); however they have been adapted for valued networks (Ziberna, 2006b). All approaches are compared on an empirical valued social network. Variants of the REGE algorithm are also compared on a few artificial valued networks in order to clarify their functionality. This is not necessary for direct approaches, which have clearly defined ideal blocks. In discussion, advantages and disadvantages of both indirect and direct approaches are discussed. [ABSTRACT FROM AUTHOR]

We describe a program for simulating symbolic interaction. The program processes verbal inputs using empirically-based equations and a cybernetic theoretical model, while making reference to dictionaries of culture measurements. Results are verbal outputs suggesting what behaviors, emotions, attributions, and labelings will occur in (he given situation. The program's structure is described by means of a pictographic algorithm. An Illustrative application uses the program with its U.S.A. and German dictionaries to analyze some problems of role directives within multi-national corporations. [ABSTRACT FROM AUTHOR]

A simple but effective neural network algorithm illustrates common principles of this new class of computational tools. Designed for use in a range of simulation studies, this minimum intelligent neural device is capable of learning which of a complex set of stimuli to avoid, and large numbers of these devices can be assembled in programs to explore the development of prejudice and of various interaction strategies. Neural nets are error-reduction algorithms with the potential to perform a wide range of useful tasks, including modeling theories of the soda! consequences of human error. [ABSTRACT FROM AUTHOR]

A comparatively simple method of uncovering the deep structure of career lines from job history data is described. Key decisions in the construction of the programming algorithm are related to substantive and theoretical ideas. Illustrations of the use of the method are offered, based on blue collar job histories from an American and a Dutch firm. Advantages, drawbacks and other applications of the program arc discussed. [ABSTRACT FROM AUTHOR]

Equivalence has become a foundational concept in social network representations of social structure. Each use of an equivalence concept has two components: (i) the definition of equivalence and (ii) a computational algorithm for detecting equivalences, or the extent to which they exist. In all substantive contexts it is necessary to determine if a particular definition of equivalence is appropriate and the extent to which the computational algorithm faithfully mirrors the equivalence definition. An extensive comparison of structural equivalence, with two structural equivalence detectors, and regular equivalence, with one regular equivalence detector, is provided for a set of social structures. As blockmodels are, among other things, hypotheses about network structure, hypotheses about structure are used to obtain the networks used for these comparisons. For any network, there is, potentially, a multiplicity of equivalences that can be mobilized so as to complement each other in analyzing social structure. [ABSTRACT FROM AUTHOR]