Embedding Node Structural Role Identity into Hyperbolic Space

TL;DR

This paper introduces a novel framework for embedding the structural roles of nodes in networks into hyperbolic space, extending existing methods to better capture complex network properties.

Contribution

It is the first to embed node structural roles into hyperbolic space, extending struct2vec with a hyperboloid model for improved network representation.

Findings

Hyperbolic space outperforms Euclidean space in capturing node structural roles.

The proposed method effectively models complex network structures.

Results are validated on multiple real-world and synthetic networks.

Abstract

Recently, there has been an interest in embedding networks in hyperbolic space, since hyperbolic space has been shown to work well in capturing graph/network structure as it can naturally reflect some properties of complex networks. However, the work on network embedding in hyperbolic space has been focused on microscopic node embedding. In this work, we are the first to present a framework to embed the structural roles of nodes into hyperbolic space. Our framework extends struct2vec, a well-known structural role preserving embedding method, by moving it to a hyperboloid model. We evaluated our method on four real-world and one synthetic network. Our results show that hyperbolic space is more effective than euclidean space in learning latent representations for the structural role of nodes.