GraphDCA -- a Framework for Node Distribution Comparison in Real and Synthetic Graphs

TL;DR

GraphDCA introduces a novel framework for comparing graphs based on node feature distributions, effectively capturing local structural similarities and differences better than traditional global statistics.

Contribution

The paper presents GraphDCA, extending Delaunay Component Analysis to graph data for evaluating graph similarity through node feature alignment.

Findings

GraphDCA accurately recognizes local structural similarities and differences.

It captures gradual changes in graph similarity under edge perturbations.

It reveals limitations of current graph generative models in reproducing local structures.

Abstract

We argue that when comparing two graphs, the distribution of node structural features is more informative than global graph statistics which are often used in practice, especially to evaluate graph generative models. Thus, we present GraphDCA - a framework for evaluating similarity between graphs based on the alignment of their respective node representation sets. The sets are compared using a recently proposed method for comparing representation spaces, called Delaunay Component Analysis (DCA), which we extend to graph data. To evaluate our framework, we generate a benchmark dataset of graphs exhibiting different structural patterns and show, using three node structure feature extractors, that GraphDCA recognizes graphs with both similar and dissimilar local structure. We then apply our framework to evaluate three publicly available real-world graph datasets and demonstrate, using gradual edge perturbations, that GraphDCA satisfyingly captures gradually decreasing similarity, unlike global statistics. Finally, we use GraphDCA to evaluate two state-of-the-art graph generative models, NetGAN and CELL, and conclude that further improvements are needed for these models to adequately reproduce local structural features.