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Network Alignment by Discrete Ollivier-Ricci Flow

  • Chien-Chun Ni
  • Yu-Yao Lin
  • Jie GaoEmail author
  • Xianfeng Gu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11282)

Abstract

In this paper, we consider the problem of approximately aligning/matching two graphs. Given two graphs \(G_{1}=(V_{1},E_{1})\) and \(G_{2}=(V_{2},E_{2})\), the objective is to map nodes \(u, v \in G_1\) to nodes \(u',v'\in G_2\) such that when uv have an edge in \(G_1\), very likely their corresponding nodes \(u', v'\) in \(G_2\) 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. 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 \(G_1\) to a node in \(G_2\) 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) (The source code of computing Ricci curvature and Ricci flow metric are available: https://github.com/saibalmars/GraphRicciCurvature).

Notes

Acknowledgement

The authors would like to thanks the funding agencies NSF DMS-1737812, CNS-1618391, CCF-1535900, DMS-1418255, and AFOSR FA9550-14-1-0193.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Yahoo! ResearchSunnyvaleUSA
  2. 2.Intel Inc.HillsboroUSA
  3. 3.Stony Brook UniversityStony BrookUSA

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