We devise an autoencoder based strategy to facilitate anomaly detection for boosted jets, employing Graph Neural Networks (GNNs) to do so. To overcome known limitations of GNN autoencoders, we design a symmetric decoder capable of simultaneously reconstructing edge features and node features. Focusing on latent space based discriminators, we find that such setups provide a promising avenue to isolate new physics and competing SM signatures from sensitivity-limiting QCD jet contributions. We demonstrate the flexibility and broad applicability of this approach using examples of $W$ bosons, top quarks, and exotic hadronically-decaying exotic scalar bosons.