Distance matrices and quadratic embedding of graphs

On the square root of quadratic matrices

Here we present a new approach to calculating the square root of a quadratic matrix. Actually, the purpose of this article is to show how the Cayley-Hamilton theorem may be used to determine an explicit formula for all the square roots of $2times 2$ matrices.

Ela on Euclidean Distance Matrices of Graphs

Received by the editors on November 13, 2011. Accepted for publication on July 8, 2013. Handling Editor: Bryan L. Shader. FMF and IMFM, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia, and IAM, University of Primorska, Slovenia ([email protected]). XLAB d.o.o., Pot za Brdom 100, 1125 Ljubljana, Slovenia, and FMF, University of Ljubljana, Slovenia ([email protected]...

On Euclidean distance matrices of graphs

The Distance Matrices of Some Graphs Related to Wheel Graphs

A simple graph G = (V, E) consists of V, a nonempty set of vertices, and E, a set of unordered pairs of distinct elements of V called edges. All graphs considered here are simple and connected. LetG be a simple connected graph with vertex set V(G) and edge set E(G).The distance between two vertices u, V ∈ V(G) is denoted by d uV and is defined as the length of the shortest path between u and V ...

Anonymisation of geographical distance matrices via Lipschitz embedding

BACKGROUND Anonymisation of spatially referenced data has received increasing attention in recent years. Whereas the research focus has been on the anonymisation of point locations, the disclosure risk arising from the publishing of inter-point distances and corresponding anonymisation methods have not been studied systematically. METHODS We propose a new anonymisation method for the release ...