A two-layer approach to analyzing imbalance in signed supply chain networks using probability-based triad census

Signed supply chain networks are essential for representing relationships between entities in commercial activities. Imbalances in these relationships can lead to significant consequences, including financial losses and reputational damage. This paper presents a two-layer analytical framework designed to identify and address imbalances in signed supply chain networks. The approach begins by mapping the initial Person-Other-X (P-O-X) layer onto the network's signed nodes, establishing a foundational framework for the analysis. Throughout the network's evolution, the method rigorously tracks its dynamics, focusing on assessing and improving the overall balance of the supply chain network. The analysis employs probability-based triad motifs to evaluate the impact of strategic sign changes on the network's structure. This provides valuable insights into how alterations to supplier-manufacturer, distributor-customer, or other critical relationships affect the network's stability. Sensitivity analysis is used to identify essential nodes or regions where sign changes substantially impact the network's structural patterns. A comparative study of the probability-based Triad Census is conducted to understand the effects of sign changes on the network structure. Key contributions include the identification of influential nodes using centrality metrics and the impact of their sign changes on structural balance. The study's findings emphasize the significant role of Betweenness Centrality in fostering balanced relationships within the supply chain network. This underscores the importance of key nodes, such as critical suppliers or distribution centers, in ensuring the overall stability and performance of the commercial network. Finally, this proactive strategy ensures a smoother flow of goods through the network, ultimately boosting performance and competitiveness in the marketplace.