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This article is a technical note on a problem frequently encountered in assessing consumer preferences. Intransitivity is seen in situations where Product a is preferred to Product b, b to c, but c to a. Inadequate preference transitivity casts suspicion on rank orders of products derived from series of paired comparisons. This problem can be given graph theoretic treatment which, although it offers no absolute solution, does make the problem clearer and emphasizes the area of the analyst's judgment. [ABSTRACT FROM AUTHOR]

Market cycles are conceptualized from the viewpoint of users. Distinctions are made between part-time and full-time traders, number of market days in a market week, location of the trader, routes used to frequent markets, the order of the good, and short-term changes in supply and demand. A number of complex market cycle types are identified with the aid of graph theoretic notions. Ecological complementarity within a market cycle framework is measurable in matrix format. An index of regional specialization can measure ecological or economic complementarity among regions. [ABSTRACT FROM AUTHOR]

This paper is addressed to the problem of locating the absolute and vertex centers (minimax criterion) of an undirected tree graph. Based upon a convexity property of the criterion function a very simple and efficient algorithm is offered that locates the minimax point by locating first a maximax point. The minimax is at the mid-point of the maximum path from the maximax point. The vertex center is located simultaneously. [ABSTRACT FROM AUTHOR]

Procedures for graphic and numerical parameter fitting from Scatchard plots for the case of two different independent sets of equivalent binding sites are described. These methods are compared with other procedures and their advantages and disadvantages are discussed. Estimates of how much one parameter can be changed without changing the Scatchard curve significantly are made. This variability of the parameters is discussed. It is shown that low saturation points are considered importance in evaluating the binding parameters of the high affinity binding site. An example of the parameter fitting procedures is given and the utility and limitations of the procedures are discussed. [ABSTRACT FROM AUTHOR]

In the context of analyzing social structures through the use of graph theory, some binary matrix operations for valued graphs are presented. These operations are demonstrated in the analysis of social network data presented by Kapferer. Further examples of where the procedures should prove useful are suggested. [ABSTRACT FROM AUTHOR]

Discusses the advantages of the graph theory and dynamic programming over decision diagrams to portray decision making problems. Background on the dynamic programming methodology; Details of a graphical portrayal of a decision making problem; Use of the decision graph developed.

The article focuses on k-class estimators which have investigated their distributional properties. The mathematical analysis of the k-class formulae rather than with their statistical analysis is presented. In this paper authors examine how the k-class estimator varies with k. They derive an expression from which the main features of the graph of a k-class estimator may be obtained and show that, except in a subspace of measure zero, the parameter estimates and their asymptotic standard errors become infinite for some value k1 that is common to the parameters of an equation whilst their ratios, the r-ratios, tend to zero. The results suggest that one should I be reluctant to choose k near k1. Indeed this is a common cause of explosive limited information maximum likelihood estimates. Second, if k1 is remote from L1 it is immediate from equation that the graph of the k-class estimate of each parameter will tend to be flat and if so the direct least squares estimate, the two stage least squares estimate and the limited information maximum likelihood estimate of each parameter will be similar.

The article presents an empirical study and inter-temporal as well as international comparisons of the behavior of the arithmetic mean of the appropriate entries of limiting matrix function. It points out the sensitivity of these interrelatedness functions to various degrees of aggregation. The problem of aggregating data from a set of multi-product firms into sectoral data has always raised very difficult statistical problems in input-output studies. The sectors must be defined as "aggregates" of closely related products. To give good predictive results the inputs must be independent of the composition of the output. For instance such independence does not exist for the flows of chromium and nickel into steel mills because they go into stainless steel but not carbon steel. In other words, a purchase order for carbon steel does not generate chromium or nickel production requirements even though the boolean product of the M matrix for this system, M 2 shows the existence of such a connection. Economists C. Yan and E. Ames measure weighs equally all connections whatever the nature of the connection.

The article focuses on a general condition for stability in demographic processes. Graph theory is employed to investigate the stability property of population transfer. The stability property is of interest because it tells us the result of indefinite repetition of a given set of transfers and helps thereby the study of the present condition. Within a population in which there exist statistically recognizable subpopulations, regions of a country, social classes, educational levels, changes within are not considered, but transfers among, such groupings. Given the rate of growth in each subpopulation and the rates of transfer among subpopulations, changes can be described by a set of differential or difference equations. A graph consists of vertices, corresponding to the states or subgroups of a population, and edges, representing transitions among states, regions, etc. Formally the vertices and edges are not defined except as points and the lines joining them. The edges will be directed, the direction indicated by an arrow. A necessary condition for ultimate stability is that the projection matrix and corresponding graph be irreducible. A matrix and its corresponding graph are irreducible in passage is possible from any vertex to any other vertex, with or without going through further vertices on the way, a graph not satisfying this condition is reducible.

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Concepts taken from graph theory and other branches of topology have been used by many sociologists and social psychologists, in particular Kurt Lewin and J. L. Moreno. Similar ideas have been used to construct statistical models of nervous systems, and these have been applied by J. S. Coleman and others to the spread of information and other soda] phenomena. The study of social networks by anthropologists has been based, knowingly or unknowingly, on the basic notions of graph theory, as has the identification and analysis of social cliques. There is little consensus among mathematicians about terminology, and social scientists have drawn fortuitously on various mathematical vocabularies as well as inventing their own technical terms. Applied to social networks, the words `connectedness' and `connectivity' may refer to properties of the distance between persons, the number of paths between them, whether there is a path at all, or the proportion of possible paths actually in existence. These different usages are contrasted by restating them all in the terminology set out in Structural models (1965) by Harary, Norman and Cartwright. [ABSTRACT FROM AUTHOR]

There is proposed a method of transforming a sutsct matrix into a graph. The method has its base on constructing a spanning tree of the graph. A criterion to decide whether a given matrix can be realized as a graph or not is described. [ABSTRACT FROM AUTHOR]

Circuit constraints on the phasing of fixed-time synchronized signal networks are defined. A method, based on a graph-theoretic approach, for deriving a fundamental set of equations characterizing these constraints is presented. [ABSTRACT FROM AUTHOR]

Hillier has described a method of selecting offsets to minimize delay in certain networks controlled by fixed-time signals. In this paper an attempt is made to extend the method by relaxing somewhat the restriction on the form of the network. The problem is expressed in terms of the theory of graphs, and an iterative process is developed for finding a set of offsets that minimizes delay over the whole network. At each stage, the part of the network already covered is extended by adding one or more links, and for the method to be viable these links must be chosen so that a certain set of intersections remains small. A method of selection of links that minimizes this set of intersections at each stage is developed. The selection of links and calculation of offsets have been programmed in Fortran. Having found one delay-minimizing set of offsets, some others that give the same total delay can be found if they exist. [ABSTRACT FROM AUTHOR]

The intent of this paper is to provide a definition of a sociometric clique in the language of graph theory. This problem is viewed from two perspectives: maintaining fidelity to the intuitive notion of a clique; and providing adequate computational mechanics for large bodies of data. Luce's (1950) concept of an n-clique is used, but further qualifications are added. Two statistics or measures with associated probability distributions are defined for testing the adequacy of a subgraph which qualifies according to the definition. [ABSTRACT FROM AUTHOR]

Describes the generation of simulated temporal patterns of vocalizations and pauses from a table of random digits in order to illustrate the misinterpretation of time series data. Graphs of actual spontaneous speech; Evidence for cognitive planning; Need to distinguish random process from causal connection.

A critical review is given of Goldberg's (1952, 1953) theory of Antigen-Antibody reactions in vitro. Goldberg's assumptions and the mathematical development of his theory are described in detail. Comparisons of Goldberg's predictions with experimental results are given in graphical form. Some criticisms are made of Goldberg's use of equations in regions in which the derivations given by him are not valid. [ABSTRACT FROM AUTHOR]

The one-parameter logistic distribution is used to illustrate certain numerical approximations for finding one- and two-stage bioassay designs which produce small posterior variances. The article discusses the use of two prior distributions, one for design and another for inference. Graphs are given for designing experiments when the prior distributions are normal. These graphs illustrate the importance of using additional dose levels when the variance of the prior distribution is large. [ABSTRACT FROM AUTHOR]

The paper presents the results of some numerical evaluations concerning the performance of the TSPRT, and characterizes the situations in which the TSPRT is superior to some alternative procedures. Graphs for the application and study of the TSPRT are also presented, and some suggestive results of additional computations are discussed The calculations are based on the formulae of T. W. Anderson [1]. [ABSTRACT FROM AUTHOR]

Focuses on the objection and modification of Koo's paper on standard results in graph theory. Development of the theory of revealed preference from a binary relation; Definition of binary relation; Demonstration on the axiom of individual demand functions.

In this tutorial the author shows how graph theory can be used to model the structural relationships in a behavioral theory. The basic elements of a graph and its related matrices are defined and illustrated. A survey of applications of graph theory in behavioral science is followed by an extensive bibliography. [ABSTRACT FROM AUTHOR]

This paper is concerned with the relation between 0–1 integer programs and graphs. An equivalence is established between solving 0–1 integer programs with quadratic or linear objective functions and solving a cut problem on a related graph. [ABSTRACT FROM AUTHOR]

This paper describes a. special class of sequencing problems called vicinal problems. They are solved by a combination of the methods of graph theory and combinatorial programming. We analyze decomposition possibilities of complete, antisymmetric graphs in order to achieve the partition of the problems into several subproblems that can be served by combinatorial programming procedures such as back-tracking and branch-and-bound. We conclude by treating a numerical example and commenting on a program written for that purpose. [ABSTRACT FROM AUTHOR]

This paper models satellite communications systems by means of bipartite graphs. It assumes stochastic inputs and time delay is the factor of interest. The paper formulates the model and describes the routing and digital transmission schemes, assuming the network links to be synchronized. Messages may be transmitted only in the synchronized time slots, on a first-come first-served basis. The queuing problem is discussed for the single branch and for the satellite network cases, and approximate solutions are obtained for the case of satellites with finite memories. [ABSTRACT FROM AUTHOR]

This paper develops the steady-state solution for the queuing system with s parallel servers when arrivals are serviced in batches of size Q. The service time for all servers is exponentially distributed and the customer inter arrival times are Erlantan of degree u. [ABSTRACT FROM AUTHOR]

This paper analyzes a Markovian queing system with balking and two heterogeneous servers determines the capacity of the slower server and obtains the optimal service rates that minimize the average characteristics of the heterogeneous system. The heterogeneous system is compared with a corresponding homogeneous system and a condition showing the efficiency of the heterogeneous system is obtained, this condition revolving only the traffic intensity and the service rates. A cost model is discussed and various tables and graphs representing the average characteristics of both the systems are given. [ABSTRACT FROM AUTHOR]

Let G be a directed graph such that ever5 edge v of G is associated with a positive integer, called the index of v. Then G is called a network graph if, at every vertex t of G, the sum of the indices of the edges terminating at v is equal to that of the edges incident from v. This paper obtains several theorems giving necessary and sufficient conditions for a directed graph to be a network graph, and applied the results to solving some problems of smoothing traffic flow. [ABSTRACT FROM AUTHOR]