# The Hidden Flow Structure and Metric Space of Network Embedding Algorithms Based on Random Walks

## TL;DR

This paper uncovers the hidden flow structure and metric space underlying random walk-based network embedding algorithms, providing theoretical insights into their effectiveness and potential applications.

## Contribution

It introduces an open-flow network model to reveal the latent metric space of random walk strategies, enhancing understanding of embedding algorithms.

## Key findings

- Reveals the flow structure of random walk algorithms
- Identifies the latent metric space underlying embeddings
- Provides theoretical explanation for embedding effectiveness

## Abstract

Network embedding which encodes all vertices in a network as a set of numerical vectors in accordance with it's local and global structures, has drawn widespread attention. Network embedding not only learns significant features of a network, such as the clustering and linking prediction but also learns the latent vector representation of the nodes which provides theoretical support for a variety of applications, such as visualization, node classification, and recommendation. As the latest progress of the research, several algorithms based on random walks have been devised. Although their high scores for learning efficiency and accuracy have drawn much attention, there is still a lack of theoretical explanation, and the transparency of the algorithms has been doubted. Here, we propose an approach based on the open-flow network model to reveal the underlying flow structure and its hidden metric space of different random walk strategies on networks. We show that the essence of embedding based on random walks is the latent metric structure defined on the open-flow network. This not only deepens our understanding of random walk based embedding algorithms but also helps in finding new potential applications in embedding.