Model-independent methods for embedding directed networks into Euclidean and hyperbolic spaces

Abstract

The arrangement of network nodes in hyperbolic spaces has become a widely studied problem, motivated by numerous results suggesting the existence of hidden metric spaces behind the structure of complex networks. Although several methods have already been developed for the hyperbolic embedding of undirected networks, approaches able to deal with directed networks are still in their infancy. Here, we propose a framework based on the dimension reduction of proximity matrices reflecting the network topology, coupled with a general conversion method transforming Euclidean node coordinates into hyperbolic ones even for directed networks. While proposing a new measure of proximity, we also incorporate an earlier Euclidean embedding method in our pipeline, demonstrating the widespread applicability of our Euclidean-hyperbolic conversion. Besides, we introduce a dimension reduction technique that maps the nodes directly into the hyperbolic space with the aim of reproducing a distance matrix measured on the given (un)directed network. According to mapping accuracy, graph reconstruction performance and greedy routing score, our methods are capable of producing high-quality embeddings for several real networks.

References in corpus (14)

• Hierarchical structure and the prediction of missing links in networks
• Community detection in networks: A user guide
• Predicting Missing Links via Local Information
• Hyperbolic Geometry of Complex Networks
• Navigability of Complex Networks
• Sustaining the Internet with Hyperbolic Mapping
• Self-similarity of complex networks and hidden metric spaces
• Evaluating Link Prediction Methods
• Directed network modules
• Emergence of Soft Communities from Geometric Preferential Attachment
• Navigability evaluation of complex networks by greedy routing efficiency
• Detecting hyperbolic geometry in networks: why triangles are not enough
• Systematic comparison of graph embedding methods in practical tasks
• Geometrical congruence and efficient greedy navigability of complex networks

Cited by in corpus (6)

• Network Alignment
• Zoo Guide to Network Embedding
• Iterative embedding and reweighting of complex networks reveals community structure
• Greedy routing optimisation in hyperbolic networks
• Symmetry-driven embedding of networks in hyperbolic space
• Nearest-neighbour directed random hyperbolic graphs