Integrating Algorithms for Complete Bipartite Graph in Network Analysis (Journal of Informatics and Mathematical Sciences, 2025)
This study aims to provide a comprehensive overview of network analysis, emphasizing the construction and application of complete bipartite graphs within organizational networks. The approach integrates both statistical and algorithmic perspectives to explore the network relationships among components in a system. In this framework, complete bipartite graphs serve as a powerful structure for implementing classical graph theory algorithms to address key problems such as game theory valuation, minimum spanning tree (MST) construction, maximum flow determination, and maximum weight matching. To address these problems, various well-established techniques are employed: the graphical method is used to solve the value of the game, Prim’s algorithm for finding the MST, the Ford-Fulkerson Algorithm for computing the maximum flow, and the Hungarian Algorithm for identifying the maximum weight matching in a complete bipartite graph. These methodologies are demonstrated through suitable numerical examples within a unified network design framework. The complete bipartite graph structure, characterized by its full interconnectedness across vertex sets, enables greater flexibility and precision in handling complex network-related problems typically encountered in organizational and operational contexts. The findings are essential for optimizing human resource allocations across departments, improving supply chain logistics by matching suppliers to distributors, balancing workloads in distributed computing systems, and enhancing communication flow in hierarchical structures. Furthermore, this model is particularly beneficial in scenarios such as task scheduling, transportation planning, and decision-making processes where interdependent entities must be efficiently paired or evaluated.