Trees, tight extensions of metric spaces, and the cohomological dimension of certain groups: A note on combinatorial properties of metric spaces

Distance spectra of graphs: A survey

Biased graphs. I. Bias, balance, and gains

In 1971, Graham and Pollack established a relationship between the number of negative eigenvalues of the distance matrix and the addressing problem in data communication systems. They also proved that the determinant of the distance matrix of a tree is a function of the number of vertices only. Since then several mathematicians were interested in studying the spectral properties of the distance matrix of a connected graph. Computing the distance characteristic polynomial and its coefficients was the first research subject of interest. Thereafter, the eigenvalues attracted much more attention. In the present paper, we report on the results related to the distance matrix of a graph and its spectral properties.

Distance Spectra of Graphs: A Survey

Multilevel modeling has grown in use over the years as a way to deal with the nonindependent nature of observations found in clustered data. However, other alternatives to multilevel modeling are available that can account for observations nested within clusters, including the use of Taylor series linearization for variance estimation, the design effect adjusted standard errors approach, and fixed effects modeling. Using 1,000 replications of 12 conditions with varied Level 1 and Level 2 sample sizes, the author compared parameter estimates, standard errors, and statistical significance using various alternative procedures. Results indicate that several acceptable procedures can be used in lieu of or together with multilevel modeling, depending on the type of research question asked and the number of clusters under investigation. Guidelines for applied researchers are discussed.

Alternatives to Multilevel Modeling for the Analysis of Clustered Data

On optimal embeddings of metrics in graphs

On matroids on edge sets of graphs with connected subgraphs as circuits II

An algorithm and its role in the study of optimal graph realizations of distance matrices

A criterion for optimality of graph realizations of distance matrices is presented. In order to illustrate the criterion’s potential, it is used to prove the optimality of several well-known graph realizations and a few new ones.

J. M. S. Simões-Pereira

Papers

On optimal embeddings of metrics in graphs

On matroids on edge sets of graphs with connected subgraphs as circuits II

An algorithm and its role in the study of optimal graph realizations of distance matrices

An optimality criterion for graph embeddings of metrics

A note on distance matrices with unicyclic graph realizations