# Link Dimension and Exact Construction of a Graph

arXiv: https://arxiv.org/abs/1906.05916 · HTML: https://mlsanity.com/paper/1906.05916/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jun 2019.

## Built on by (most cited first, 1 of 1)

- [Graph Coordinates and Conventional Neural Networks -- An Alternative for Graph Neural Networks](https://mlsanity.com/paper/2312.01342/) (2023)

## Abstract (arXiv)

Minimum resolution set and associated metric dimension provide the basis for unique and systematic labeling of nodes of a graph using distances to a set of landmarks. Such a distance vector set, however, may not be unique to the graph and does not allow for its exact construction. The concept of construction set is presented, which facilitates the unique representation of nodes and the graph as well as its exact construction. Link dimension is the minimum number of landmarks in a construction set. Results presented include necessary conditions for a set of landmarks to be a construction set, bounds for link dimension, and guidelines for transforming a resolution set to a construction set.