Beyond ranking nodes: Predicting epidemic outbreak sizes by network centralities.

Area of Science:

• Network epidemiology
• Graph theory
• Computational social science

Background:

• Identifying critical nodes for disease spread is essential in network epidemiology.
• Existing studies often rank nodes within specific networks, not predict importance across all possible networks.
• Node position, using standard network measures, is explored for predictive power.

Purpose of the Study:

• To assess how well standard network measures predict a node's epidemiological importance across all possible graphs of a given size.
• To establish a benchmark for epidemiological importance using exact expected outbreak size.
• To overcome limitations of specific graph models or datasets by examining all nonisomorphic graphs.

Main Methods:

• Exhaustive analysis of all ten-node nonisomorphic graphs.
• Calculation of exact expected outbreak size as a benchmark for epidemiological importance.
• Evaluation of various combinations of network centralities (e.g., PageRank, Katz centrality, edge-sensitive measures).

Main Results:

• Combinations of two or more centralities achieved high predictive accuracy (R2 ≥ 0.91).
• Successful combinations typically included a normalized spectral centrality and a measure sensitive to graph edges.
• Predictive performance remained strong even under challenging epidemic simulation parameters.

Conclusions:

• Network centrality measures, when combined, offer robust predictions of a node's role in disease spreading.
• Spectral and edge-sensitive centralities are key components for accurate prediction models.
• This approach provides a generalizable method for identifying important nodes in epidemiological networks.