# Centrality anomalies in complex networks as a result of model over-simplification

## TL;DR

This paper demonstrates that centrality anomalies in complex networks, such as transportation networks, often result from overly simplified models that ignore weights and spatial constraints, and that more sophisticated models reduce these anomalies.

## Contribution

It shows that centrality anomalies are due to model over-simplification and advocates for using more detailed models with weights and spatial data to accurately identify key nodes.

## Key findings

- Weighted models reduce the number of centrality anomalies.
- Unweighted projections exhibit significant anomalies compared to null models.
- Model sophistication correlates with anomaly reduction.

## Abstract

Tremendous advances have been made in our understanding of the properties and evolution of complex networks. These advances were initially driven by information-poor empirical networks and theoretical analysis of unweighted and undirected graphs. Recently, information-rich empirical data complex networks supported the development of more sophisticated models that include edge directionality and weight properties, and multiple layers. Many studies still focus on unweighted undirected description of networks, prompting an essential question: how to identify when a model is simpler than it must be? Here, we argue that the presence of centrality anomalies in complex networks is a result of model over-simplification. Specifically, we investigate the well-known anomaly in betweenness centrality for transportation networks, according to which highly connected nodes are not necessarily the most central. Using a broad class of network models with weights and spatial constraints and four large data sets of transportation networks, we show that the unweighted projection of the structure of these networks can exhibit a significant fraction of anomalous nodes compared to a random null model. However, the weighted projection of these networks, compared with an appropriated null model, significantly reduces the fraction of anomalies observed, suggesting that centrality anomalies are a symptom of model over-simplification. Because lack of information-rich data is a common challenge when dealing with complex networks and can cause anomalies that misestimate the role of nodes in the system, we argue that sufficiently sophisticated models be used when anomalies are detected.