TopoLa: a novel embedding framework for understanding complex networks

TL;DR

TopoLa introduces a new embedding framework that leverages global topological structures of complex networks within hyperbolic spaces, improving analysis and deep learning applications.

Contribution

It presents TopoLa, a novel method encoding topological information into hyperbolic embeddings, enhancing network analysis and deep learning models.

Findings

Topological structure correlates with node positioning in latent space.

TopoLa improves analysis of both conventional and low-rank networks.

Enhanced deep learning models using TopoLa distance.

Abstract

Complex networks, which are the abstractions of many real-world systems, present a persistent challenge across disciplines for people to decipher their underlying information. Recently, hyperbolic geometry of latent spaces has gained traction in network analysis, due to its ability to preserve certain local intrinsic properties of the nodes. In this study, we explore the problem from a much broader perspective: understanding the impact of nodes' global topological structures on latent space placements. Our investigations reveal a direct correlation between the topological structure of nodes and their positioning within the latent space. Building on this deep and strong connection between node distance and network topology, we propose a novel embedding framework called Topology-encoded Latent Hyperbolic Geometry (TopoLa) for analyzing complex networks. With the encoded topological information in the latent space, TopoLa is capable of enhancing both conventional and low-rank networks, using the singular value gap to clarify the mathematical principles behind this enhancement. Meanwhile, we show that the equipped TopoLa distance can also help augment pivotal deep learning models encompassing knowledge distillation and contrastive learning.