  Stress models are a promising approach for graph drawing. They minimize the
weighted sum of the squared errors of the Euclidean and desired distances for
each node pair. The desired distance typically uses the graph-theoretic
distances obtained from the all-node pair shortest path problem. In a minimized
stress function, the obtained coordinates are affected by the non-Euclidean
property and the high-dimensionality of the graph-theoretic distance matrix.
Therefore, the graph-theoretic distances used in stress models may not
necessarily be the best metric for determining the node coordinates. In this
study, we propose two different methods of adjusting the graph-theoretical
distance matrix to a distance matrix suitable for graph drawing while
preserving its structure. The first method is the application of eigenvalue
decomposition to the inner product matrix obtained from the distance matrix and
the obtainment of a new distance matrix by setting some eigenvalues with small
absolute values to zero. The second approach is the usage of a stress model
modified by adding a term that minimizes the Frobenius norm between the
adjusted and original distance matrices. We perform computational experiments
using several benchmark graphs to demonstrate that the proposed method improves
some quality metrics, including the node resolution and the Gabriel graph
property, when compared to conventional stress models.
