GraphGen: A Scalable Approach to Domain-agnostic Labeled Graph Generation

Abstract

Graph generative models have been extensively studied in the data mining literature. While traditional techniques are based on generating structures that adhere to a pre-decided distribution, recent techniques have shifted towards learning this distribution directly from the data. While learning-based approaches have imparted significant improvement in quality, some limitations remain to be addressed. First, learning graph distributions introduces additional computational overhead, which limits their scalability to large graph databases. Second, many techniques only learn the structure and do not address the need to also learn node and edge labels, which encode important semantic information and influence the structure itself. Third, existing techniques often incorporate domainspecific rules and lack generalizability. Fourth, the experimentation of existing techniques is not comprehensive enough due to either using weak evaluation metrics or focusing primarily on synthetic or small datasets. In this work, we develop a domain-agnostic technique called GraphGen to overcome all of these limitations. Graph-Gen converts graphs to sequences using minimum DFS codes. Minimum DFS codes are canonical labels and capture the graph structure precisely along with the label information. The complex joint distributions between structure and semantic labels are learned through a novel LSTM architecture. Extensive experiments on million-sized, real graph datasets show GraphGen to be 4 times faster on average than state-of-the-art techniques while being significantly better in quality across a comprehensive set of 11 different metrics. Our code is released at: https://github.com/idea-iitd/graphgen.

A Systematic Survey on Deep Generative Models for Graph Generation

“…Ideally, high-quality generated graphs should be diverse and similar, but not identical. Thus, uniqueness is utilized to capture the diversity of generated graphs [6,44,79,92,107]. To calculate the uniqueness of a generated graph, the generated graphs that are sub-graph isomorphic to some other generated graphs are first removed.…”

“…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.…”

“…Consequentially, most existing works merely focus on small graphs, typically with dozens to thousands of nodes [24,34,47,79,113,119,140]. However, many real-world networks are large, with millions to billions of nodes [44], such as the Internet, biological neuronal networks, and social networks. It is important for any generative model to scale to large graph.…”

Compressed graph representation for scalable molecular graph generation

“…A major challenge for molecular graph generation is addressing the scalability issue caused by its high computational complexity [4]. The representation of a molecular graph G = (V, E) on which a model learns, where V and E are the set of nodes and edges in G , typically involves an adjacency expression between its nodes, yielding O(|V| 2 ) complexity.…”

“…You et al presented GraphRNN which constructs a model on a node-level sequence representation with M-dimensional adjacency vectors, where M is set to less than |V| , by employing breadth-firstsearch node ordering with which the complexity is reduced to O(|V|M) [10]. Goyal et al presented Graph-Gen which transforms a molecular graph into an edgelevel sequence based on minimum depth-first-search coding, which leads to a complexity of O(|E|) [4]. However, as in the SMILES representation, the sequential nature imposes constraints on the model architecture and prevents the model from capturing molecular similarity and retaining chemical validity.…”