GraphGen is an autoregressive graph generation model that represents graphs as sequences of canonical orderings and uses deep recurrent networks to learn the distribution over graph structures, generating novel graphs one edge at a time following a minimum DFS (depth-first search) code ordering. GraphGen improves upon GraphRNN by using a more compact and canonical graph representation that reduces the sequence length and eliminates ordering ambiguity.

Why GraphGen Matters in AI/ML: GraphGen addresses the graph ordering ambiguity problem in autoregressive graph generation—since a graph of N nodes has N! possible orderings—by using canonical minimum DFS codes that provide a unique, compact representation, enabling more efficient and accurate generative modeling.

• Minimum DFS code — Each graph is represented by its minimum DFS code: the lexicographically smallest sequence obtained by performing DFS traversals from all possible starting nodes; this provides a canonical (unique) ordering that eliminates the N! ordering ambiguity • Edge-level autoregression — GraphGen generates graphs edge by edge (rather than node by node like GraphRNN), where each step adds an edge defined by (source_node, target_node, edge_label); this is more granular than node-level generation and captures edge-level dependencies • LSTM-based generator — A multi-layer LSTM processes the sequence of DFS code edges and predicts the next edge at each step; the model learns P(e_t | e_1, ..., e_{t-1}) using teacher forcing during training and autoregressive sampling during generation • Compact representation — The minimum DFS code is significantly shorter than the adjacency matrix flattening used by other methods: for a graph with N nodes and E edges, the DFS code has O(E) entries versus O(N²) for full adjacency matrices • Graph validity — By construction, the DFS code ordering ensures that generated sequences always correspond to valid, connected graphs; invalid edge additions are prevented by the generation grammar, eliminating the need for post-hoc validity filtering

GraphGen advances autoregressive graph generation through minimum DFS code representations that provide canonical, compact graph orderings, enabling edge-level generation with guaranteed connectivity and eliminating the ordering ambiguity that limits other sequential graph generation methods.