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Graph Transformation, Specifications, and Nets pp 83–104Cite as

A Tutorial on Graph Transformation

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10800))

Abstract

Graph transformation or graph rewriting has been developed for nearly 50 years and has become a mature and manifold formal technique. Basically, rewrite rules are used to manipulate graphs. These rules are given by a left-hand side and a right-hand side graph and the application comprises matching the left-hand side and replacing it with the right-hand side of the rule.

In this contribution we give a tutorial on graph transformation that explains the so-called double-pushout approach to graph transformation in a rigorous, but non-categorical way, using a gluing construction. We explicate the definitions with several small examples.

We also introduce attributes and attributed graph transformation in a lightweight form. The paper is concluded by a more extensive example on a leader election protocol, the description of tool support and pointers to related work.

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Notes

  1. 1.

    Note that considerable part of graph transformation theory is concerned with making the results independent of the specific graph structure under consideration (see [28, 30]). This however depends on the use of category theory and we will not follow this path here.

  2. 2.

    The morphism n need not be injective, hence an edge e might have several preimages under n. In this case, it is possible that the new attribute of an edge cannot be uniquely determined.

  3. 3.

    http://groove.cs.utwente.nl/.

  4. 4.

    http://groove.cs.utwente.nl/wp-content/uploads/leader-electiongps.zip.

  5. 5.

    http://www.user.tu-berlin.de/o.runge/agg/.

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Acknowledgements

We would like to thank all the participants of the North German GraTra Day in February 2017 in Hamburg for the discussion about this paper. Especially, we would like to acknowledge Berthold Hoffmann, Leen Lambers and Hans-Jörg Kreowski who contributed by commenting on our paper and giving valuable suggestions and hints.

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Authors and Affiliations

  1. Universität Duisburg-Essen, Duisburg, Germany

    Barbara König & Dennis Nolte

  2. Hochschule für Angewandte Wissenschaften Hamburg, Hamburg, Germany

    Julia Padberg

  3. University of Twente, Enschede, Netherlands

    Arend Rensink

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  1. Barbara König
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  2. Dennis Nolte
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  4. Arend Rensink
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Correspondence to Dennis Nolte .

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Editors and Affiliations

  1. Department of Informatics, University of Leicester, Leicester, United Kingdom

    Reiko Heckel

  2. Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, Marburg, Germany

    Gabriele Taentzer

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König, B., Nolte, D., Padberg, J., Rensink, A. (2018). A Tutorial on Graph Transformation. In: Heckel, R., Taentzer, G. (eds) Graph Transformation, Specifications, and Nets. Lecture Notes in Computer Science(), vol 10800. Springer, Cham. https://doi.org/10.1007/978-3-319-75396-6_5

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