Estimating Network Dimension When the Spectrum Struggles

TL;DR

This paper introduces a novel method for estimating the dimension of a network by leveraging an efficient algorithm based on nearest neighbor distances, applicable to both weighted and unweighted networks, and compares it to spectral gap methods.

Contribution

It adapts a data cloud algorithm for network dimension estimation, extending its applicability to unweighted networks with spectral embedding, offering a more efficient alternative to spectral gap analysis.

Findings

The proposed method accurately estimates network dimension.

It outperforms spectral gap approaches in certain scenarios.

The technique is applicable to both weighted and unweighted networks.

Abstract

What is the dimension of a network? Here, we view it as the smallest dimension of Euclidean space into which nodes can be embedded so that pairwise distances accurately reflect the connectivity structure. We show that a recently proposed and extremely efficient algorithm for data clouds, based on computing first and second nearest neighbour distances, can be used as the basis of an approach for estimating the dimension of a network with weighted edges. We also show how the algorithm can be extended to unweighted networks when combined with spectral embedding. We illustrate the advantages of this technique over the widely-used approach of characterising dimension by visually searching for a suitable gap in the spectrum of the Laplacian.