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vertex representations

Vertex representations, often referred to as node embeddings, are low-dimensional vector encodings of individual vertices within a graph network that capture their structural roles, connectivity patterns, and relational properties. By mapping discrete nodes into a continuous mathematical space, these vectors preserve vital topological information, including local neighborhood proximities and broader network structures. This transformation allows standard machine learning and statistical models to directly process complex graph data, facilitating downstream analytical tasks such as node classification, link prediction, clustering, and network visualization without relying on manual feature engineering.

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GraRep: Learning Graph Representations with Global Structural Information

GraRep: Learning Graph Representations with Global Structural Information

Shaosheng Cao, Wei Lu, Qiongkai Xu

OrganizationsAustralian National UniversityIBMSingapore University of Technology and DesignXidian University

Why you should read this

Proposes GraRep, a graph representation learning model that captures high-order relational information by directly factorizing distinct k-step probability transition matrices to preserve global graph structure across separate subspaces without sampling.

In this paper, we present GraRep, a novel model for learning vertex representations of weighted graphs. This model learns low dimensional vectors to represent vertices appearing in a graph and, unlike existing work, integrates global structural information of the graph into the learning process. We also formally analyze the connections between our work and several previous research efforts, including the DeepWalk model of Perozzi et al. [20] as well as the skip-gram model with negative sampling of Mikolov et al. [18] We conduct experiments on a language network, a social network as well as a citation network and show that our learned global representations can be effectively used as features in tasks such as clustering, classification and visualization. Empirical results demonstrate that our representation significantly outperforms other state-of-the-art methods in such tasks.

Added

2026-09-24