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Graph representation learning plays an important role in many graph miningapplications, but learning embeddings of large-scale graphs remains a problem.Recent works try to improve scalability via graph summarization -- i.e., theylearn embeddings on a smaller summary graph, and then restore the nodeembeddings of the original graph. However, all existing works depend onheuristic designs and lack theoretical analysis.  Different from existing works, we contribute an in-depth theoretical analysisof three specific embedding learning methods based on introduced kernel matrix,and reveal that learning embeddings via graph summarization is actuallylearning embeddings on a approximate graph constructed by the configurationmodel. We also give analysis about approximation error. To the best of ourknowledge, this is the first work to give theoretical analysis of thisapproach. Furthermore, our analysis framework gives interpretation of someexisting methods and provides great insights for future work on this problem.

Learning node embeddings via summary graphs: a brief theoretical analysis