Column Graphs Research Articles

Information design and manipulation

We discuss the results of an investigation into the graphic reporting practices used by 240 leading UK companies in their 1989 corporate annual reports. Our main findings are that 79 per cent of companies used graphs and that 64 per cent of all graphs were bar/ column graphs. Many of these were poorly designed and constructed. There was evidence of biasing in graphic choices, with the use of graphic presentation being contingent upon 'good' rather than 'bad' financial performance. Companies were three times more likely to include graphs in their annual report which exaggerated, rather than understated, favourable time series trends in key performance variables. There was also evidence of the use of certain design and construction techniques intended to create a favourable visual impression. There is a need for more studies of graphic practices in other domains, and for guidelines to raise the standards and fidelity of financial graphs.

Inverting graphs of rectangular matrices

This paper addresses the question of determining the class of rectangular matrices having a given graph as a row or column graph. We also determine equivalent conditions on a given pair of graphs in order for them to be the row and column graphs of some rectangular matrix. In connection with these graph inversion problems we discuss the concept of minimal inverses. This concept turns out to have two different forms in the case of one-graph inversion. For the two-graph case we present a method of determining when an inverse is minimal. Finally we apply the two-graph theorem to a class of energy related matrices.

Inverting Signed Graphs

This paper addresses the question of determining the class of rectangular matrices having a given signed graph as a signed row or column graph. We also determine equivalent conditions on a given pair of signed graphs in order for them to be the signed row and column graphs of some rectangular matrix. In connection with these signed graph inversion problems we discuss the concept of minimality and illustrate how to invert a pair of signed graphs.

Rectangular Matrices and Signed Graphs

This paper extends the theory of graphs associated with real rectangular matrices to include information about the signs of the elements. We show when signed row and column graphs can be defined for the matrix A. We also deduce conditions under which these graphs are balanced. This leads to a definition of the class of quasi-Morishima rectangular matrices A. It is shown that the Perron–Frobenius theorem applies to the matrices $AA^T $ and $A^T A$ when A is a quasi-Morishima matrix. Finally we examine the applications of our results to several classes of matrices occurring in energy economic models. All results in this paper are purely qualitative in character.

Projection Methods for Solving Sparse Linear Systems

Some methods of successive approximation for the solution of simultaneous linear equations are discussed. The coefficient matrix A of the linear system is assumed to be sparse. It is shown that savings in the computer storage and the computing time are possible, if there exists a subset of the rows (columns) of A, consisting of only orthogonal rows (columns). Such savings are also possible, if for some permutation matrices P and Q, PAQ has a particular structure, viz., singly bordered block diagonal form. It is shown that the set of orthogonal rows (columns) of A, as well as P and Q can be determined by using some results from graph theory (e.g., incidence matrices, row and column graphs, points of attachment). Geometrical interpretations of the methods and their inter-relatiohip are given.