In the field of medical applications, graph theory offers diverse topological models for representing the human heart. The key challenge is identifying the optimal structure as an effective diagnostic model. This paper explains the rationale behind using topological visualization, graph analysis, and rough sets via neighborhood systems. We introduce the novel $1$-neighborhood system ( $1$- $NS$) tools, enabling rough set generalization and a heart topological graph model. Exploring minimal and core minimal neighborhoods, vital for classifying subsets and accuracy computation, these approaches outperform existing methods while preserving Pawlak's properties. Multiple topologies are constructed and examined using these systems. The paper presents a real-world example showcasing innovative topological spaces through a human heart's vertex network. These spaces enhance understanding of the heart's structural organization. Two algorithms are introduced for decision-making and generating graph topologies, defining unique spaces. Beyond graph theory, these techniques apply to medical contexts like blood circulation and geographical scenarios such as community street mapping. Implemented using MATLAB, they are valuable tools.