Spectral Graph Complexity

TL;DR

This paper introduces a spectral measure of graph complexity based on Weyl's law and demonstrates its correlation with the graph's embeddability in low-dimensional Euclidean space.

Contribution

It presents a novel spectral complexity measure for graphs and explores its relationship with low-dimensional embeddings.

Findings

Spectral complexity correlates with embedding quality.

The measure provides insights into graph structure.

Experimental validation supports the proposed notion.

Abstract

We introduce a spectral notion of graph complexity derived from the Weyl's law. We experimentally demonstrate its correlation to how well the graph can be embedded in a low-dimensional Euclidean space.