Edge-based sequential graph generation with recurrent neural networks

Abstract

Graph generation with MachineLearning is an open problem with applications in various research fields. In this work, we propose to cast the generative process of a graph into a sequential one, relying on a node ordering procedure. We use this sequential process to design a novel generative model composed of two recurrent neural networks that learn to predict the edges of graphs: the first network generates one endpoint of each edge, while the second network generates the other endpoint conditioned on the state of the first. We test our approach extensively on five different datasets, comparing with two well-known baselines coming from graph literature, and two recurrent approaches, one of which holds state of the art performances. Evaluation is conducted considering quantitative and qualitative characteristics of the generated samples. Results show that our approach is able to yield novel, and unique graphs originating from very different distributions, while retaining structural properties very similar to those in the training sample. Under the proposed evaluation framework, our approach is able to reach performances comparable to the current state of the art on the graph generation task.

Deep Graph Generators: A Survey

“…In addition to the methods discussed so far, there also exist other approaches adopting an edge-based generation strategy. Bacciu et al [28] propose to generate a sequence of edges for each graph instead of generating graphs node-by-node. They first convert a graph G under the node ordering π to an ordered edge sequence S edge, π = [S…”

“…Although the most remarkable application of modern graph generation approaches explored so far is generating molecular structures, several other non-application-specific approaches have been proposed [25], [28], [30], [36], [41], [55], [61] working on more general datasets. While these methods' ultimate goal is to be used on real-world applications such as generating social network graphs, most of them suffer from scalability issues.…”

Deep learning for graphs

“…This is typically achieved by sampling a matrix of node embeddings H, using it to compute an affinity matrix  = H • H T , and then recovering the actual adjacencies from the affinity matrix [24,28]. Second, decoders that generate graphs by a sequence of edits [27,29,30,31], e.g., by first decoding a single node and then connecting it to existing nodes, as illustrated in Figure 3. The former approach requires the size of the graph being known in advance, whereas the latter approach requires that some order in which edits occur is provided at training time.…”

A Systematic Survey on Deep Generative Models for Graph Generation

“…Novelty. Novelty measures the percentage of generated graphs that are not sub-graphs of the training graphs and vice versa [6,44,92]. Note that identical graphs are defined as graphs that are sub-graph isomorphic to each other.…”