Spectral Graph Wavelets for Structural Role Similarity in Networks

by   Claire Donnat, et al.

Nodes residing in different parts of a graph can have similar structural roles within their local network topology. The identification of such roles provides key insight into the organization of networks and can also be used to inform machine learning on graphs. However, learning structural representations of nodes is a challenging unsupervised-learning task, which typically involves manually specifying and tailoring topological features for each node. Here we develop GraphWave, a method that represents each node's local network neighborhood via a low-dimensional embedding by leveraging spectral graph wavelet diffusion patterns. We prove that nodes with similar local network neighborhoods will have similar GraphWave embeddings even though these nodes may reside in very different parts of the network. Our method scales linearly with the number of edges and does not require any hand-tailoring of topological features. We evaluate performance on both synthetic and real-world datasets, obtaining improvements of up to 71


page 1

page 2

page 3

page 4


Ego-based Entropy Measures for Structural Representations

In complex networks, nodes that share similar structural characteristics...

RiWalk: Fast Structural Node Embedding via Role Identification

Nodes performing different functions in a network have different roles, ...

Perfectly Secure Communication, based on Graph-Topological Addressing in Unique-Neighborhood Networks

We consider network graphs G=(V,E) in which adjacent nodes share common ...

Ego-based Entropy Measures for Structural Representations on Graphs

Machine learning on graph-structured data has attracted high research in...

Digraphwave: Scalable Extraction of Structural Node Embeddings via Diffusion on Directed Graphs

Structural node embeddings, vectors capturing local connectivity informa...

SNoRe: Scalable Unsupervised Learning of Symbolic Node Representations

Learning from real-life complex networks is a lively research area, with...

Local, global and scale-dependent node roles

This paper re-examines the concept of node equivalences like structural ...