The role of the decoder is to reconstruct certain graph statistics from the node
embeddings that are generated by the encoder.

San Jose State University

Encoder and decoder graph framework is used for learning node embeddings for graph representation learning.

Encoder maps node in a graph to a low dimensional vector space.

Decoder uses the low dimensional node embeddings to reconstruct the node's position in the original graph.

Encoder and Decoder Graph Framework 

Hamilton, W.L. Graph Representation Learning. *Synthesis Lectures on Artificial Intelligence and Machine Learning*. 2020, 14(3), 1–159. https://doi.org/10.2200/S01045ED1V01Y202009AIM046

Graph Representation Learning by William Hamilton

Decoder Framework in Shallow Embedding Approach

The encoder is a function that maps nodes $v \in \mathcal{V}$ to vector embeddings
$ z_v \in {\rm I\!R}^d$
(where $z_v$ corresponds to the embedding for node $v \in \mathcal{V}$).

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