# Efficient Algorithms for Attributed Graph Alignment with Vanishing Edge Correlation

arXiv: https://arxiv.org/abs/2308.09210 · HTML: https://mlsanity.com/paper/2308.09210/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Aug 2023.

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

- [Counting Cycles with AI: Counting Cycles with AI: Computationally Efficient Equivalent Forms with Applications](https://mlsanity.com/paper/2505.17964/) (2025)

## Abstract (arXiv)

Graph alignment refers to the task of finding the vertex correspondence between two correlated graphs of n vertices. Extensive study has been done on polynomial-time algorithms for the graph alignment problem under the ErdHos-R'enyi graph pair model, where the two graphs are ErdHos-R'enyi graphs with edge probability qu, correlated under certain vertex correspondence. To achieve exact recovery of the correspondence, all existing algorithms at least require the edge correlation coefficient ρu between the two graphs to be non-vanishing as nrightarrow∞. Moreover, it is conjectured that no polynomial-time algorithm can achieve exact recovery under vanishing edge correlation ρu<1/polylog(n). In this paper, we show that with a vanishing amount of additional attribute information, exact recovery is polynomial-time feasible under vanishing edge correlation ρu ≥ n-Theta(1). We identify a local tree structure, which incorporates one layer of user information and one layer of attribute information, and apply the subgraph counting technique to such structures. A polynomial-time algorithm is proposed that recovers the vertex correspondence for most of the vertices, and then refines the output to achieve exact recovery. The consideration of attribute information is motivated by real-world applications like LinkedIn and Twitter, where user attributes like birthplace and education background can aid alignment.