This repository was crated for initial analysis of Graph Neural Networks on hypergraphs. The main goal is a comparison of results between hypergraphs and graphs using different data representation and different models.

Data are stored in Grakn (grakn.ai) - open-source knowledge graph. It is designed to store data represented as a hypergraph. It enables to create hyperedges which are non-pair wise relationships. Moreover, hyperedges can link other hyperedges. Considering these features from Data Representation point of view, Grakn provides an opportunity to build a rich data structure, which can be further 'flatten' to less expresive forms.

As the initial analysis is conducted on relatively small graphs, the whole queried subgraphs can be stored without a concern of size of data because of it's redundancy. Raw queried data are stored in a following format:

• columns contain queried nodes and hyperedges types
• rows contain singular subgraph (path) returned by query

In this repository these data are stored in csv files raw_relationship_data.csv in each directory for a specific dataset e.g. for biograkn these data will be present in 'hypergraph_nn/hypergraph_nn/data/biograkn' directory after running script. Similarily script for running load for a specific dataset can be found in a directory for this dataset e.g. for biograkn these data will be present in 'hypergraph_nn/hypergraph_nn/data/biograkn'.

There are following scripts for data transormation:

• 'data_transformer.py' - data are transormed to edges index - two columns - one for source node and one for target node.
• 'get_nodes_labels.py' - data are transformed to csv with two columns - one for node id and one for node label
• 'ids_encoder.py' - nodes ids are encoded to be within the range 0..N-1 where N is the number of nodes. It's required for some PyTorch models.

At the final step PyTorch 'Dataset' class is created for each of the dataset, in order to work seamlessly with PyTorch models.

• biograkn covid - initial dataset for testing. Contains data from Biograkn COVID, which is a knowledge graph with COVID-19 related data link.

So far no features has been added and GNN Stack learns relationships based on graph structure

• GCNConv - described in “Semi-supervised Classification with Graph Convolutional Networks” paper. PyTorch GCNConv model
• GraphSAGE - described in "Inductive Representation Learning on Large Graphs” paper. PyTorch SAGEConv model
• GAT - desribed in “Graph Attention Networks” paper. PyTorch SAGEConv model
• HypergraphConv - described in “Hypergraph Convolution and Hypergraph Attention” paper. PyTorch HypergraphConv model
• HyperGraphConv extension

This model is a slightly modified version of the original HypergraphConv model in order to adjust it to Grakn type of hypergraph. This model assumption is that it considers hyperedges which are linked by other hyperedges as vertices (meta-vertices). Let G = (V',E) be a hypergraph, where V' is a set of any 'entity' which is linked by any relationship and E is a set of hyperedges. In this case, number of instances of V' is equal to number of vertices entities and hyperedges inluded in other higher hyperrelationships - |V'| = |V_n| + |V_e|, where |V_n| is the number of actual nodes (vertices) and |V_e| is the number of hyperedges linked by other hyperedges.

In order to be in consonance with the original paper the following notation is used: N' = |V'|

Finally, all of the calculations in the paper with regards to N and V should be replaced with respectively N' and V'.

This slight modification leads embedded hyperedges (hyperedges linked by other hyperedges) to have their own feature vector. If a given set of hyperedges doesn't have any straightforward features the feature vector might consist of values 1.

In order to assess the influence of hypergraphs data representation on graph algorithms, there is a need to define different data representation types which can be applied to the same datasets, which allows for comparison. The following types has been defined to meet these criteria.

Data are stored in a casual pair-wise graph. Hyperrelations are removed and replaced by pair-wise relations in a following manner:

• hyperrelation which links N nodes is replaced by pair-wise relations between all of these N nodes - number of created edges: N(N – 1)/2

This representation is reffered as casual_graph in a code.

Data from a given hypergraph (can be Grakn type of hypergraph) are stored in a pair-wise graph where:

• hyperrelations become nodes in a pair-wise graph and all vertices related by a given hyperrelation have now pair-wise edges with a hyperrelation represented as a node

This representation is referred as hypergraph_to_graph in a code.

Data are represented as a classic definition of hypergraph. It's hyperedges are non pair-wise and can link more than 2 edges. Yet, it doesn't allow a hyperedge to link other hyperedges. Data from Grakn hypergraph are mapped in a following way:

• all related hyperedges are merged to one and nodes that they link are now linked by (one) newly created merged hyperedge

This representation is referred as hypergraph in a code.

This is the starting method of data representation. Hyperedges can link many nodes (or other hyperedges). They can also link hyperedges with nodes.

This representation is referred as grakn_hypergraph in a code.

• hypergraph_nn/hypergraph_nn/
  • data - devided further into subdirectories for datasets. Each subdirectory contains scripts and files for Data Load and Transformation (described in 'Load' and 'Transformation' in 'Data Pipeline' section)
  • datasets - devided further into subdirectories for datasets. Each subdirectory contains scripts and files for PyTorch Datasets (described in 'PyTorch Dataset' in 'Data Pipeline' section)
  • models - contains scripts for GNN models (described in 'Models' section)

In order to run these examples one needs to have Python 3 installed.

Required packages can be installed from 'requirement.txt' file using pip using the following command:

pip install -r requirements.txt

In order to run data pipeline navigate to 'hypergraph_nn/hypergraph_nn/data/biograkn/' and run 'data_pipeline.sh'.

Once data pipeline has been run, 'run.sh' script can be executed to run training loops for each model.