connecting graphs with r-hypermodules via normal fuzzy subhypermodules

In this paper, we analyze the connection between r-hypermodules and graphs by associating a graph with an r- hypermodule through a normal fuzzy subhypermodule. we investigate the graph’s properties, including connectedness, completeness, eulerian and hamiltonian characteristics. by defining a regular relation based on the fuzzy  subhypermodule, we study how algebraic properties of r-hypermodules induence the associated graph. this work contributes to the understanding of fuzzy algebraic structures and their graphical representations, with potential applications in computer science and network theory.