NetLSD: Hearing the Shape of a Graph

TL;DR

NetLSD introduces a novel graph comparison method that is invariant to node order and size, scalable, and captures the graph's shape through spectral signatures, outperforming previous methods in efficiency and expressiveness.

Contribution

It presents the first scalable, permutation- and size-invariant spectral graph descriptor that effectively compares large graphs based on their shape.

Findings

Outperforms previous methods in expressiveness.

Demonstrates high efficiency on real-world graphs.

Provides a scalable approach for large graph comparison.

Abstract

Comparison among graphs is ubiquitous in graph analytics. However, it is a hard task in terms of the expressiveness of the employed similarity measure and the efficiency of its computation. Ideally, graph comparison should be invariant to the order of nodes and the sizes of compared graphs, adaptive to the scale of graph patterns, and scalable. Unfortunately, these properties have not been addressed together. Graph comparisons still rely on direct approaches, graph kernels, or representation-based methods, which are all inefficient and impractical for large graph collections. In this paper, we propose the Network Laplacian Spectral Descriptor (NetLSD): the first, to our knowledge, permutation- and size-invariant, scale-adaptive, and efficiently computable graph representation method that allows for straightforward comparisons of large graphs. NetLSD extracts a compact signature that inherits the formal properties of the Laplacian spectrum, specifically its heat or wave kernel; thus, it hears the shape of a graph. Our evaluation on a variety of real-world graphs demonstrates that it outperforms previous works in both expressiveness and efficiency.