What are graph embeddings?

Graph embeddings are the transformation of property graphs to a vector or a set of vectors. They encode the structural and semantic information of the graph, enabling downstream machine learning algorithms to operate on them. The primary objective of graph embeddings is to capture the underlying patterns and properties of the graph, facilitating various tasks.

In essence, graph embeddings transform the graph data from a discrete, symbolic representation into a continuous, numerical representation, which traditional machine learning models or deep learning architectures can efficiently process. The main advantage of graph embeddings lies in their ability to preserve both the local neighborhood information (i.e., the direct connections of each node) and the global structural patterns of the entire graph.

A graph embedding is typically a vector with float values, and the user can predetermine its size.

For example, if we have a graph with 20 nodes and choose an embedding size of 7, the resulting embedding matrix shape would be (20, 7). These numbers encode the geometric relationships present in the original graph.

Need of graph embeddings

Graph embeddings address the challenges associated with graph data analysis and machine learning tasks. Graphs are widely used to represent complex relationships in various real-world domains, such as social networks, biological networks, recommendation systems, and knowledge graphs. However, raw graph data is often high-dimensional, sparse, and lacks the structural patterns necessary for traditional machine learning algorithms to effectively process and extract meaningful insights.

Graph embeddings provide a solution by transforming the nodes and edges of a graph into low-dimensional vectors while preserving important structural information. This transformation enables traditional machine learning algorithms, like deep learning and graph-based models, to be applied more effectively to graph data.

Graph representation learning

The process of learning graph embeddings is referred to as graph representation learning. It involves learning a mapping function $f: G → R^n$, where $f$ learns the graph’s local and global geometric properties in the form of a low-dimensional representation with a size of $n$. There are two main types of graph embeddings:

• node embeddings ($f: V → R^n$)

• edge embeddings ($f: E → R^n$)

The choice between these embeddings depends on the specific machine learning task.

Applications of graph embeddings

Graph embeddings have found applications in various domains due to their versatile nature. Some of the prominent use cases include:

• Node classification: Graph embeddings can be employed for classifying nodes in the graph into predefined categories based on their structural properties and attributes.

• Link prediction: By learning representations of nodes and edges, graph embeddings can be utilized to predict missing or potential connections between nodes in the graph.

• Recommender systems: Graph embeddings have proven beneficial for building personalized recommender systems, where nodes represent users and items, and edges indicate interactions or preferences.

• Community detection: Graph embeddings can help identify clusters or communities within the graph, assisting in understanding the underlying structure and relationships.

• Graph generation: By sampling embeddings from a learned distribution, one can generate new graph structures that exhibit similar properties to the original graph.

• Drug discovery and bioinformatics: Graph embeddings have shown promise in representing molecular structures, protein interactions, and biological pathways, accelerating drug discovery processes.

• Natural Language Processing (NLP): Graph embeddings can enhance NLP tasks by incorporating structured knowledge from knowledge graphs into language models.

Python packages for graph embeddings

Various Python packages are available to facilitate the implementation of graph embeddings. Some of the notable ones include:

• karateclub: This library provides implementations of multiple graph embedding algorithms, making it a versatile choice.

• graphvite: Graphvite includes implementations of popular methods like DeepWalk, LINE, and node2vec, along with knowledge graph embedding methods.

• GraphEmbedding: This package offers a range of algorithms, including DeepWalk, LINE, node2vec, SDNE, and struc2vec, catering to diverse embedding needs.

• GEM: GEM is a comprehensive library that covers Laplacian Eigenmaps, locally linear embedding, graph factorization, and several other embedding techniques.

Conclusion

Graph embeddings enable machine learning techniques to be applied to graph-structured data. By converting complex graphs into low-dimensional vector representations, graph embeddings facilitate various tasks like link prediction, node classification, and visualization. With the help of popular Python libraries and different embedding algorithms, we can leverage graph embeddings to gain insights and make predictions in a wide range of applications.