# Unifying Structural Proximity and Equivalence for Enhanced Dynamic Network Embedding

arXiv: https://arxiv.org/abs/2503.19926 · HTML: https://mlsanity.com/paper/2503.19926/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 57 references that are in the map.
- First posted on arXiv 14 Mar 2025.

## Builds on (most cited first, 21 of 21)

- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [struc2vec: Learning Node Representations from Structural Identity](https://mlsanity.com/paper/1704.03165/) (2017)
- [Structure-Aware Transformer for Graph Representation Learning](https://mlsanity.com/paper/2202.03036/) (2022)
- [Graph Embedding Techniques, Applications, and Performance: A Survey](https://mlsanity.com/paper/1705.02801/) (2017)
- [A Survey on Network Embedding](https://mlsanity.com/paper/1711.08752/) (2017)
- [Dynamic Graph Representation with Knowledge-aware Attention for Histopathology Whole Slide Image Analysis](https://mlsanity.com/paper/2403.07719/) (2024)
- [Node Embedding over Temporal Graphs](https://mlsanity.com/paper/1903.08889/) (2019)
- [Dynamic Network Embedding Survey](https://mlsanity.com/paper/2103.15447/) (2021)
- [Dynamic Scenario Representation Learning for Motion Forecasting with Heterogeneous Graph Convolutional Recurrent Networks](https://mlsanity.com/paper/2303.04364/) (2023)
- [T-EDGE: Temporal WEighted MultiDiGraph Embedding for Ethereum Transaction Network Analysis](https://mlsanity.com/paper/1905.08038/) (2019)
- [Data on face-to-face contacts in an office building suggests a low-cost vaccination strategy based on community linkers](https://mlsanity.com/paper/1409.7017/) (2014)
- [A Survey of Graph Transformers: Architectures, Theories and Applications](https://mlsanity.com/paper/2502.16533/) (2025)
- [K-Core based Temporal Graph Convolutional Network for Dynamic Graphs](https://mlsanity.com/paper/2003.09902/) (2020)
- [Adaptive Sign Algorithm for Graph Signal Processing](https://mlsanity.com/paper/2201.05821/) (2022)
- [Exploring the structure and function of temporal networks with dynamic graphlets](https://mlsanity.com/paper/1412.3885/) (2014)
- [Embedding Node Structural Role Identity into Hyperbolic Space](https://mlsanity.com/paper/2011.01512/) (2020)
- [Dynamic networks reveal key players in aging](https://mlsanity.com/paper/1307.3388/) (2013)
- [STWalk: Learning Trajectory Representations in Temporal Graphs](https://mlsanity.com/paper/1711.04150/) (2017)

## Abstract (arXiv)

Dynamic network embedding methods transform nodes in a dynamic network into low-dimensional vectors while preserving network characteristics, facilitating tasks such as node classification and community detection. Several embedding methods have been proposed to capture structural proximity among nodes in a network, where densely connected communities are preserved, while others have been proposed to preserve structural equivalence among nodes, capturing their structural roles regardless of their relative distance in the network. However, most existing methods that aim to preserve both network characteristics mainly focus on static networks and those designed for dynamic networks do not explicitly account for inter-snapshot structural properties. This paper proposes a novel unifying dynamic network embedding method that simultaneously preserves both structural proximity and equivalence while considering inter-snapshot structural relationships in a dynamic network. Specifically, to define structural equivalence in a dynamic network, we use temporal subgraphs, known as dynamic graphlets, to capture how a node's neighborhood structure evolves over time. We then introduce a temporal-structural random walk to flexibly sample time-respecting sequences of nodes, considering both their temporal proximity and similarity in evolving structures. The proposed method is evaluated using five real-world networks on node classification where it outperforms benchmark methods, showing its effectiveness and flexibility in capturing various aspects of a network.