Title: Expanding the Katz Index for Link Prediction: A Case Study on a Live Fish Movement Network

Abstract: In aquaculture, disease spread models often neglect the dynamic interactions between farms, hindering accuracy. This study enhances the Katz index (KI) to incorporate spatial and temporal patterns of fish movement, improving the prediction of farms susceptible to disease via live fish transfers. We modified the Katz index to create models like the Weighted Katz Index (WKI), Edge Weighted Katz Index (EWKI), and combined models (e.g., KIEWKI). These incorporate spatial distances and temporal movement patterns for a comprehensive aquaculture network connection prediction framework. Model performance was evaluated using precision, recall, F1-scores, AUPR, and AUROC. The EWKI model significantly outperformed the traditional KI and other variations. It achieved high precision (0.988), recall (0.712), F1-score (0.827), and AUPR (0.970). Combined models (KIEWKI, WKIEWKI) approached, but couldn't surpass, EWKI performance. This study highlights the value of extending Katz index models to improve disease spread predictions in aquaculture networks. The EWKI model's performance demonstrates an innovative and flexible approach to tackling spatial challenges within network analysis.