The impact of partially missing communities~on the reliability of centrality measures

TL;DR

This study examines how the reliability of centrality measures in networks is affected by missing nodes, especially when missing nodes are concentrated within the same community, revealing nuanced effects in different network types.

Contribution

It provides new insights into the reliability of centrality measures under community-aware missing node scenarios across different network models.

Findings

Centrality measures are more reliable when missing nodes are community-concentrated.

Betweenness centrality is less reliable in scale-free networks with community-based missing nodes.

Stronger community structure improves reliability in scale-free networks.

Abstract

Network data is usually not error-free, and the absence of some nodes is a very common type of measurement error. Studies have shown that the reliability of centrality measures is severely affected by missing nodes. This paper investigates the reliability of centrality measures when missing nodes are likely to belong to the same community. We study the behavior of five commonly used centrality measures in uniform and scale-free networks in various error scenarios. We find that centrality measures are generally more reliable when missing nodes are likely to belong to the same community than in cases in which nodes are missing uniformly at random. In scale-free networks, the betweenness centrality becomes, however, less reliable when missing nodes are more likely to belong to the same community. Moreover, centrality measures in scale-free networks are more reliable in networks with stronger community structure. In contrast, we do not observe this effect for uniform networks. Our observations suggest that the impact of missing nodes on the reliability of centrality measures might not be as severe as the literature suggests.