A Multi-purposed Unsupervised Framework for Comparing Embeddings of Undirected and Directed Graphs

Graph embedding is a transformation of nodes of a network into a set of vectors. A good embedding should capture the underlying graph topology and structure, node-to-node relationship, and other relevant information about the graph, its subgraphs, and nodes themselves. If these objectives are achieved, an embedding is a meaningful, understandable, and often compressed representation of a network. Unfortunately, selecting the best embedding is a challenging task and very often requires domain experts. In this paper, we extend the framework for evaluating graph embeddings that was recently introduced by the authors. Now, the framework assigns two scores, local and global, to each embedding that measure the quality of an evaluated embedding for tasks that require good representation of local and, respectively, global properties of the network. The best embedding, if needed, can be selected in an unsupervised way, or the framework can identify a few embeddings that are worth further investigation. The framework is flexible, scalable, and can deal with undirected/directed, weighted/unweighted graphs.

Evaluating Node Embeddings of Complex Networks

Graph embedding is a transformation of nodes of a graph into a set of vectors. A~good embedding should capture the graph topology, node-to-node relationship, and other relevant information about the graph, its subgraphs, and nodes. If these objectives are achieved, an embedding is a meaningful, understandable, compressed representations of a network that can be used for other machine learning tools such as node classification, community detection, or link prediction. The main challenge is that one needs to make sure that embeddings describe the properties of the graphs well. As a result, selecting the best embedding is a challenging task and very often requires domain experts. In this paper, we do a series of extensive experiments with selected graph embedding algorithms, both on real-world networks as well as artificially generated ones. Based on those experiments we formulate two general conclusions. First, if one needs to pick one embedding algorithm before running the experiments, then node2vec is the best choice as it performed best in our tests. Having said that, there is no single winner in all tests and, additionally, most embedding algorithms have hyperparameters that should be tuned and are randomized. Therefore, our main recommendation for practitioners is, if possible, to generate several embeddings for a problem at hand and then use a general framework that provides a tool for an unsupervised graph embedding comparison. This framework (introduced recently in the literature and easily available on GitHub repository) assigns the divergence score to embeddings to help distinguish good ones from bad ones.