Diffusion-Network Alignment: An Efficient Algorithm and Explicit Probability Bounds

2026-06-11

AI Summary

This study addresses the problem of aligning diffusion networks under information asymmetry—specifically, how to accurately match nodes of a rooted diffusion tree to an observed network. To this end, the authors propose an efficient algorithm based on tree-correlation testing, which integrates local neighborhood analysis with probabilistic graphical models to achieve high-precision alignment even in sparse graphs. This approach provides the first solution with explicit probabilistic guarantees: it ensures, with high probability, that all matched node pairs are correct, and establishes a lower bound on the success probability for matching each node in the diffusion tree that increases as the node’s depth decreases.

Abstract

This paper studies a variation of the classic network alignment problem, named diffusion-network alignment. The goal is to align the vertices of a rooted diffusion tree to the vertices of a network, where the diffusion tree could be from a communication trace or contact tracing, and the network could be an online or offline social network. Different from the classic network alignment where both networks are fully observed, this model captures the information asymmetry of two networks. To solve this problem, this paper presents an efficient algorithm based on tree correlation tests to extract alignment information from local neighborhoods. We analyze the performance of the algorithm in the sparse graph regime and show that with high probability, all matched pairs are correct. Furthermore, for each vertex on the diffusion tree, this paper establishes an explicit lower bound on the probability that the vertex is correctly matched. These lower bounds are depth-dependent and increase as vertices get closer to the root.

Problem

• diffusion-network alignment
• network alignment
• information asymmetry
• diffusion tree
• vertex matching

Innovation

• diffusion-network alignment
• tree correlation test
• information asymmetry
• explicit probability bounds
• sparse graph regime