Deep Graph Mapper: Seeing Graphs Through the Neural Lens.

Area of Science:

• Computational topology
• Graph theory
• Machine learning

Background:

• Graph summarization faces challenges with arbitrary data structures, unlike grid-like image data.
• Existing pooling methods may not fully capture complex graph topologies.

Purpose of the Study:

• To develop topologically grounded graph summaries using the Mapper algorithm and graph neural networks (GNNs).
• To establish Mapper as a generalized framework for graph pooling.
• To introduce novel pooling algorithms and visualize complex networks.

Main Methods:

• Integration of the Mapper algorithm with graph neural networks (GNNs).
• Mathematical proof demonstrating Mapper as a generalization of soft cluster assignment pooling.
• Development and application of new pooling algorithms.

Main Results:

• The proposed method provides topologically grounded graph summaries.
• Mapper is proven to be a generalization of existing soft cluster assignment pooling methods.
• Novel pooling algorithms achieve competitive performance against state-of-the-art methods.
• Successful generation of GNN-aided visualizations for complex networks.

Conclusions:

• The Mapper algorithm offers a powerful and flexible topological framework for graph pooling.
• This approach facilitates the design of effective and novel graph pooling strategies.
• The method enhances the interpretability and visualization of complex network data through GNNs.