2018/09/02 by Chien-Chun Ni, Yu-Yao Lin, Ni, Chien-Chun +6 · 2 citations
Computer Science · Physics and Astronomy · #Complex Network Analysis Techniques #Computational Geometry (cs.CG) #FOS: Computer and information sciences #Graph Theory and Algorithms #Social and Information Networks (cs.SI) #Topological and Geometric Data Analysis #cs.CG #cs.SI
paper · pdf · doi:10.48550/arxiv.1809.00320
Appears in the Proceedings of the 26th International Symposium on Graph Drawing and Network Visualization (GD 2018)
openalex publication_date 2018/09/02 · arxiv created 2018/09/07 · arxiv updated 2018/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.