Attributed Graph Alignment

TL;DR

This paper investigates the attributed graph alignment problem, integrating user attributes with graph structure to improve vertex correspondence recovery, providing theoretical limits and conditions for success.

Contribution

It introduces the attributed graph alignment problem and derives matching achievability and converse results, bridging models based solely on connections and those based on attributes.

Findings

Exact recovery conditions established for various parameter regimes.

Results unify models using only connections and only attributes.

Theoretical bounds for graph alignment with attributes derived.

Abstract

Motivated by various data science applications including de-anonymizing user identities in social networks, we consider the graph alignment problem, where the goal is to identify the vertex/user correspondence between two correlated graphs. Existing work mostly recovers the correspondence by exploiting the user-user connections. However, in many real-world applications, additional information about the users, such as user profiles, might be publicly available. In this paper, we introduce the attributed graph alignment problem, where additional user information, referred to as attributes, is incorporated to assist graph alignment. We establish both the achievability and converse results on recovering vertex correspondence exactly, where the conditions match for certain parameter regimes. Our results span the full spectrum between models that only consider user-user connections and models where only attribute information is available.