# Network Alignment by Discrete Ollivier-Ricci Flow

arXiv: https://arxiv.org/abs/1809.00320 · HTML: https://mlsanity.com/paper/1809.00320/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Sep 2018.

## Built on by (most cited first, 14 of 14)

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- [Enhancing Graph Representation Learning with Localized Topological Features](https://mlsanity.com/paper/2501.09178/) (2025)
- [CurvGAD: Leveraging Curvature for Enhanced Graph Anomaly Detection](https://mlsanity.com/paper/2502.08605/) (2025)
- [Tackling Over-smoothing on Hypergraphs: A Ricci Flow-guided Neural Diffusion Approach](https://mlsanity.com/paper/2603.15696/) (2026)
- [Efficient Curvature-aware Graph Network](https://mlsanity.com/paper/2511.01443/) (2025)
- [FadMan: Federated Anomaly Detection across Multiple Attributed Networks](https://mlsanity.com/paper/2205.14196/) (2022)
- [Geometry matters: insights from Ollivier Ricci Curvature and Ricci Flow into representational alignment through Ollivier-Ricci Curvature and Ricci Flow](https://mlsanity.com/paper/2501.00919/) (2025)
- [Dynamic Graph Structure Learning via Resistance Curvature Flow](https://mlsanity.com/paper/2601.08149/) (2026)
- [Geometric Flow enhanced Graph Coarsening](https://mlsanity.com/paper/2609.14962/) (2026)
- [Ironing the Graphs: Toward a Correct Geometric Analysis of Large-Scale Graphs](https://mlsanity.com/paper/2407.21609/) (2024)
- [Geometric Evolution Graph Convolutional Networks: Enhancing Graph Representation Learning via Ricci Flow](https://mlsanity.com/paper/2603.26178/) (2026)

## Abstract (arXiv)

In this paper, we consider the problem of approximately aligning/matching two graphs. Given two graphs G1=(V1,E1) and G2=(V2,E2), the objective is to map nodes u, v ∈ G1 to nodes u',v'∈ G2 such that when u, v have an edge in G1, very likely their corresponding nodes u', v' in G2 are connected as well. This problem with subgraph isomorphism as a special case has extra challenges when we consider matching complex networks exhibiting the small world phenomena. In this work, we propose to use `Ricci flow metric', to define the distance between two nodes in a network. This is then used to define similarity of a pair of nodes in two networks respectively, which is the crucial step of network alignment. %computed by discrete graph curvatures and graph Ricci flows. Specifically, the Ricci curvature of an edge describes intuitively how well the local neighborhood is connected. The graph Ricci flow uniformizes discrete Ricci curvature and induces a Ricci flow metric that is insensitive to node/edge insertions and deletions. With the new metric, we can map a node in G1 to a node in G2 whose distance vector to only a few preselected landmarks is the most similar. The robustness of the graph metric makes it outperform other methods when tested on various complex graph models and real world network data sets (Emails, Internet, and protein interaction networks)footnoteThe source code of computing Ricci curvature and Ricci flow metric are available: https://github.com/saibalmars/GraphRicciCurvature.