Optimizing Resource Allocation in Two-Section Hypergraphs: A Maximal Flow Analysis Approach

Hypergraphs extend the traditional graph model by allowing edges to connect multiple nodes, offering a more realistic representation of complex transportation scenarios. The modelling process involves defining nodes to represent origins, destinations, and intermediate points, with hyperedges indicating potential transportation paths and associated capacities. The paper details the steps of the max-flow analysis, including source and sink designation, capacity assignment, bottleneck identification, and resource allocation optimization. This paper investigates the application of maximum flow algorithms to identify the maximal flow from a source node to a sink node using a 2-section of the hypergraph.