Flow-Driven Fusion Edge Selection for Network Integration Inspired by Physarum polycephalum

Abstract: Background: Adaptive structural changes in biological systems have inspired a range of network optimization algorithms, particularly for problems where global reconfiguration is impractical. In network design, integrating multiple independently constructed networks requires the effective selection of fusion edges to ensure stable and efficient connectivity. Objective: This study examines the adaptive network formation behavior of the slime mold Physarum polycephalum and proposes a heuristic fusion edge selection method based on flow-driven conductivity dynamics. Methods: The proposed method enables localized network integration by selecting candidate fusion edges based on the characteristic transport properties that emerge within the network. Results: Numerical simulations on random mesh networks demonstrate that the method effectively forms fusion paths between isolated networks and accelerates flow concentration along the resulting paths, even in heterogeneous network environments. The results further indicate that appropriate control of both the selection and the number of added edges is crucial for efficient network fusion under flow-conserved dynamics. Conclusions: Although the proposed method does not explicitly optimize shortest path length and involves several hyperparameters, it provides a flexible framework for network fusion based on local interactions. These findings suggest that biologically inspired, flow-based heuristics offer a promising approach for integrating complex networks when global optimization is infeasible. Keywords: Network Fusion, Edge Selection, Physarum-Inspired Optimization, Flow-Based Heuristics, Graph Networks.