UniqueRank: Identifying Important and Difficult-to-Replace Nodes in Attributed Graphs

TL;DR

UniqueRank is a novel node-ranking method that combines attribute uniqueness and structural importance to identify crucial nodes in attributed graphs, especially those that are hard to replace, with applications in social, terrorist, supply chain, and biomolecular networks.

Contribution

The paper introduces UniqueRank, a Markov-Chain-based approach that considers attribute dissimilarity alongside structural importance to identify nodes that are difficult to replace.

Findings

UniqueRank effectively identifies important nodes with dissimilar attributes.

Removing top UniqueRank nodes causes larger efficiency reductions in real networks.

UniqueRank can identify structurally critical atoms in biomolecular structures.

Abstract

Node-ranking methods that focus on structural importance are widely used in a variety of applications, from ranking webpages in search engines to identifying key molecules in biomolecular networks. In real social, supply chain, and terrorist networks, one definition of importance considers the impact on information flow or network productivity when a given node is removed. In practice, however, a nearby node may be able to replace another node upon removal, allowing the network to continue functioning as before. This replaceability is an aspect that existing ranking methods do not consider. To address this, we introduce UniqueRank, a Markov-Chain-based approach that captures attribute uniqueness in addition to structural importance, making top-ranked nodes harder to replace. We find that UniqueRank identifies important nodes with dissimilar attributes from its neighbors in simple symmetric networks with known ground truth. Further, on real terrorist, social, and supply chain networks, we demonstrate that removing and attempting to replace top UniqueRank nodes often yields larger efficiency reductions than removing and attempting to replace top nodes ranked by competing methods. Finally, we show UniqueRank's versatility by demonstrating its potential to identify structurally critical atoms with unique chemical environments in biomolecular structures.