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Learning distributed representations for nodes in graphs is a crucialprimitive in network analysis with a wide spectrum of applications. Lineargraph embedding methods learn such representations by optimizing the likelihoodof both positive and negative edges while constraining the dimension of theembedding vectors. We argue that the generalization performance of thesemethods is not due to the dimensionality constraint as commonly believed, butrather the small norm of embedding vectors. Both theoretical and empiricalevidence are provided to support this argument: (a) we prove that thegeneralization error of these methods can be bounded by limiting the norm ofvectors, regardless of the embedding dimension; (b) we show that thegeneralization performance of linear graph embedding methods is correlated withthe norm of embedding vectors, which is small due to the early stopping of SGDand the vanishing gradients. We performed extensive experiments to validate ouranalysis and showcased the importance of proper norm regularization inpractice.

The Importance of Norm Regularization in Linear Graph Embedding: Theoretical Analysis and Empirical Demonstration