In a world of rapidly evolving data structures and interconnected systems, traditional flat or singly-nested graph models often fall short in capturing the true complexity of real-world data. Hierarchical structures and dependencies, a common feature in many domains including biology, social networks, manufacturing processes, and more, cannot be accurately captured by these conventional approaches. Recursive_GNN emerges as a solution to this challenge by offering a flexible and versatile tool that models and embeds arbitrarily nested graphs, making it capable of capturing complex, hierarchical systems with unprecedented precision.

The versatility of Recursive_GNN makes it a powerful tool across a wide array of domains, some of which include:

1. Chemistry and Material Science: Molecules can be represented as graphs, where atoms are nodes and bonds are edges. The complex structure of molecules and sub-molecules can be modeled accurately with our Recursive_GNN.

2. Computer Networks: Networks can be represented as graphs of sub-networks. Recursive_GNN can capture the inherent structure, providing valuable insights into network dynamics and operations.

3. Hierarchical Social Networks: Social structures can be broken down into individuals, groups, and communities, forming a nested graph. Recursive_GNN can represent these hierarchical social networks with high fidelity.

4. Biological Systems: From ecosystems to genetic or neural networks, the intricate relationships and hierarchical nature of these systems can be modeled using Recursive_GNN, potentially leading to new discoveries.

5. Supply Chains and Manufacturing Processes: Recursive_GNN can model supply chain networks, capturing the hierarchical dependencies among suppliers, manufacturers, distributors, and retailers.

6. Software Systems: Software architectures and function calls form a nested graph structure, which can be modeled and analyzed using Recursive_GNN.

Recursive_GNN works by employing a novel recursive approach that computes embeddings for nodes in a graph and its sub-graphs. The algorithm is initialized by assigning random embeddings to the nodes. Then, for each node, if it has a nested graph, the same computation is performed on the nested graph recursively. The current node's embedding and the aggregate embedding of the nested graph (if present) are then combined to form the final embedding for the node. The recursion unravels the nested graph hierarchy, ensuring that all levels of complexity are addressed and captured in the final model.

Here is a high-level pseudocode representation of the Recursive_GNN algorithm:

1. function RECURSIVE_GNN(graph G):
2.    for each node v in G do
3.        if v has a nested graph G' then
4.            embedding_G' = RECURSIVE_GNN(G')
5.        else
6.            embedding_G' = None
7.        end if
8.        embedding_v = COMBINE(node_function(v), AGGREGATE({embedding_u for u in Neighbors(v)}), embedding_G')
9.    end for
10.   return AGGREGATE({embedding_v for v in G})

This repository contains the implementation of Recursive_GNN. Here's a breakdown of the contents:

1. recursive_gnn.py: The core implementation of the Recursive_GNN algorithm.

2. utils.py: Utility functions used for data loading, preprocessing, and post-processing.

3. node_functions.py: Different node function implementations that can be used with Recursive_GNN.

4. combine_functions.py: Different combine function implementations that can be used with Recursive_GNN.

5. aggregate_functions.py: Different aggregate function implementations that can be used with Recursive_GNN.

6. examples/: Example usage of Recursive_GNN on various datasets.

7. tests/: Unit tests to ensure the correctness of the implementation.

To use Recursive_GNN, follow these steps:

1. Clone the repository

git clone https://github.com/username/Recursive_GNN.git

2. Navigate to the cloned repository

cd Recursive_GNN

3. Install the necessary requirements

pip install -r requirements.txt

4. Run the examples

python examples/example.py

We invite researchers and developers to explore this repository, use Recursive_GNN in their projects, and join us in improving and expanding its capabilities.

If you use Recursive_GNN in your research, please use the following BibTeX entry.

@misc{Andersson2023,
  author = {Samuel M. Andersson},
  title = {Recursive_GNN: A Novel Recursive Approach for Graph Embedding},
  year = {2023},
  publisher = {GitHub},
  journal = {GitHub Repository},
  howpublished = {\url{https://github.com/username/Recursive_GNN}},
}