Sensitivity and Reliability in Incomplete Networks: Centrality Metrics to Community Scoring Functions

TL;DR

This study evaluates how missing data affects network analysis metrics, finding that permanence is most robust for community scoring and centrality measures, with implications for message spreading in noisy networks.

Contribution

It introduces a comprehensive evaluation of sensitivity and reliability of network parameters under noise, highlighting permanence as the most effective metric.

Findings

Permanence outperforms other metrics in noisy conditions.

Closeness centrality is a close second for sensitivity.

Permanence's top vertices remain stable for message spreading despite noise.

Abstract

Network analysis is an important tool in understanding the behavior of complex systems of interacting entities. However, due to the limitations of data gathering technologies, some interactions might be missing from the network model. This is a ubiquitous problem in all domains that use network analysis, from social networks to hyper-linked web networks to biological networks. Consequently, an important question in analyzing networks is to understand how increasing the noise level (i.e. percentage of missing edges) affects different network parameters. In this paper we evaluate the effect of noise on community scoring and centrality-based parameters with respect to two different aspects of network analysis: (i) sensitivity, that is how the parameter value changes as edges are removed and (ii) reliability in the context of message spreading, that is how the time taken to broadcast a message changes as edges are removed. Our experiments on synthetic and real-world networks and three different noise models demonstrate that for both the aspects over all networks and all noise models, permanence qualifies as the most effective metric. For the sensitivity experiments closeness centrality is a close second. For the message spreading experiments, closeness and betweenness centrality based initiator selection closely competes with permanence. This is because permanence has a dual characteristic where the cumulative permanence over all vertices is sensitive to noise but the ids of the top-rank vertices, which are used to find seeds during message spreading remain relatively stable under noise.