# Network Dependence Testing via Diffusion Maps and Distance-Based Correlations

## TL;DR

This paper introduces a new method for testing network dependence using diffusion maps and distance-based correlations, providing theoretical guarantees and practical effectiveness in identifying key graph embeddings.

## Contribution

The paper presents a novel dependence testing approach that combines diffusion maps with distance-based correlations, with proven consistency and efficiency in high-dimensional network data.

## Key findings

- Consistent test statistic under mild assumptions
- Efficient identification of informative graph embeddings
- Validated on simulated and real network data

## Abstract

Deciphering the associations between network connectivity and nodal attributes is one of the core problems in network science. The dependency structure and high-dimensionality of networks pose unique challenges to traditional dependency tests in terms of theoretical guarantees and empirical performance. We propose an approach to test network dependence via diffusion maps and distance-based correlations. We prove that the new method yields a consistent test statistic under mild distributional assumptions on the graph structure, and demonstrate that it is able to efficiently identify the most informative graph embedding with respect to the diffusion time. The methodology is illustrated on both simulated and real data.