Spectral Graph Forge: Graph Generation Targeting Modularity

TL;DR

The paper introduces Spectral Graph Forge, a novel method for generating synthetic graphs that accurately replicate the community structure of real networks by leveraging spectral properties of the modularity matrix.

Contribution

It presents a spectral-based approach for graph generation that preserves modularity and other structural properties, outperforming existing methods in accuracy and randomness.

Findings

Outperforms state-of-the-art in modularity accuracy

Preserves local structural properties and node attributes

Enables extensions to target other network properties

Abstract

Community structure is an important property that captures inhomogeneities common in large networks, and modularity is one of the most widely used metrics for such community structure. In this paper, we introduce a principled methodology, the Spectral Graph Forge, for generating random graphs that preserves community structure from a real network of interest, in terms of modularity. Our approach leverages the fact that the spectral structure of matrix representations of a graph encodes global information about community structure. The Spectral Graph Forge uses a low-rank approximation of the modularity matrix to generate synthetic graphs that match a target modularity within user-selectable degree of accuracy, while allowing other aspects of structure to vary. We show that the Spectral Graph Forge outperforms state-of-the-art techniques in terms of accuracy in targeting the modularity and randomness of the realizations, while also preserving other local structural properties and node attributes. We discuss extensions of the Spectral Graph Forge to target other properties beyond modularity, and its applications to anonymization.