reviews: 
Comments: Overall, the paper provides valuable contributions and should be accepted, though it requires both minor and significant revisions. I have given a lower score to ensure that all issues are addressed. The paper effectively tackles the challenge of defining the underlying combinatorial graph, which is crucial for performing accurate analysis and properly separating point clouds.
Strengths: Here’s an expanded version of your statement:

"The paper presents a pioneering approach for constructing an underlying combinatorial graph for a given point cloud, addressing several crucial challenges in graph-based data representation. The proposed method ensures key properties such as connectivity, sparsity of the graph, and the ability to accurately reconstruct the original point cloud. These properties are essential for both efficient computation and the preservation of the inherent structure of the data.

By focusing on these aspects, the authors effectively balance the need for a graph that is sufficiently sparse—thereby reducing computational complexity—while still maintaining connectivity, which is necessary for capturing the relationships between points in the cloud. This delicate balance is often difficult to achieve, as sparse graphs may lose critical information, and densely connected graphs can lead to inefficiency and overfitting. The authors’ method overcomes this trade-off and ensures that the graph retains the essential features of the point cloud, enabling reliable downstream analysis.

Additionally, the paper demonstrates how the performance of existing methods can be significantly improved by replacing the traditional graph construction techniques with the newly proposed combinatorial graph. The empirical results presented show notable enhancements in areas such as classification accuracy, clustering performance, and point cloud segmentation, underscoring the practical benefits of the new graph structure. These improvements are a testament to the robustness and effectiveness of the method, positioning it as a valuable tool for a wide range of applications in fields such as computer vision, machine learning, and graph signal processing.

The introduction of this novel graph construction framework represents a substantial step forward in the field, potentially opening new avenues for research on graph-based point cloud analysis. It not only improves existing methodologies but also provides a foundation for further exploration of how combinatorial structures can be leveraged to better understand and manipulate high-dimensional data."
Weaknesses: The main weakness of the paper is that the proposed graph construction is not continuous and doesn't operate on a pre-existing attributed graph. Instead, it creates its own selected graph, which may limit its applicability in cases where the underlying graph already contains valuable domain-specific information. This approach lacks flexibility, especially in scenarios where a smooth transition or integration with existing graph structures is required. As a result, the method may overlook important attributes or contextual details in real-world applications, reducing its versatility. The main concern is that the point cloud may become copolar and thus, the convex hull would become 2-dimensional. Does it happen in real-world datasets?
Recommendation: 8
Reviewer confidence: 5
Soundness/correctness: 3
Clarity: 3