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 $v \in \mathcal{V}$).

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

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

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