Spectral Alignment of Graphs

Soheil Feizi, Gerald Quon, Mariana Recamonde-Mendoza, Muriel Medard, Manolis Kellis, Ali Jadbabaie

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


Graph alignment refers to the problem of finding a bijective mapping across vertices of two graphs such that, if two nodes are connected in the first graph, their images are connected in the second graph. This problem arises in many fields, such as computational biology, social sciences, and computer vision and is often cast as a quadratic assignment problem (QAP). Most standard graph alignment methods consider an optimization that maximizes the number of matches between the two graphs, ignoring the effect of mismatches. We propose a generalized graph alignment formulation that considers both matches and mismatches in a standard QAP formulation. This modification can have a major impact in aligning graphs with different sizes and heterogeneous edge densities. Moreover, we propose two methods for solving the generalized graph alignment problem based on spectral decomposition of matrices. We compare the performance of proposed methods with some existing graph alignment algorithms including Natalie2, GHOST, IsoRank, NetAlign, Klau's approach as well as a semidefinite programming-based method over various synthetic and real graph models. Our proposed method based on simultaneous alignment of multiple eigenvectors leads to consistently good performance in different graph models. In particular, in the alignment of regular graph structures, which is one of the most difficult graph alignment cases, our proposed method significantly outperforms other methods.

Original languageEnglish (US)
Article number8698885
Pages (from-to)1182-1197
Number of pages16
JournalIEEE Transactions on Network Science and Engineering
Issue number3
StatePublished - Jul 1 2020


  • Graph Alignment
  • Graph Matching
  • Quadratic Assignment Problem
  • Spectral Graph Methods

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Computer Networks and Communications


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