On the Expressive Power of Linear Algebra on Graphs

Author Floris Geerts

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Floris Geerts
  • University of Antwerp, Antwerp, Belgium

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Floris Geerts. On the Expressive Power of Linear Algebra on Graphs. In 22nd International Conference on Database Theory (ICDT 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 127, pp. 7:1-7:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


Most graph query languages are rooted in logic. By contrast, in this paper we consider graph query languages rooted in linear algebra. More specifically, we consider MATLANG, a matrix query language recently introduced, in which some basic linear algebra functionality is supported. We investigate the problem of characterising equivalence of graphs, represented by their adjacency matrices, for various fragments of MATLANG. A complete picture is painted of the impact of the linear algebra operations in MATLANG on their ability to distinguish graphs.

Subject Classification

ACM Subject Classification
  • Information systems → Query languages
  • Mathematics of computing → Graph theory
  • Theory of computation → Logic
  • matrix query languages
  • graph queries
  • graph theory
  • logics


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