Categorical Foundations of Distributed Graph Transformation

  • Hartmut Ehrig
  • Fernando Orejas
  • Ulrike Prange
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4178)


A distributed graph (N,D) consists of a network graph N and a commutative diagram D over the scheme N which associates local graphs D(n i ) and graph morphisms D(e): D(n 1) →D(n 2) to nodes n 1, n 2 and edges e: n 1n 2 in N.

Although there are several interesting applications of distributed graphs and transformations, even the basic pushout constructions for the double pushout approach of distributed graph transformation could be shown up to now only in very special cases.

In this paper we show that the category of distributed graphs can be considered as a Grothendieck category over a specific indexed category, which assigns to each network N the category of all diagrams D of shape N. In this framework it is possible to give a free construction which allows to construct for each diagram D 1 over N 1 and network morphism h:N 1N 2 a free extension F h (D 1) over N 2 and to show that the Grothendieck category is complete and cocomplete if the underlying category of local graphs has these properties.

Moreover, an explicit construction for general pushouts of distributed graphs is given. This pushout construction is based on the free construction. The non-trivial proofs for free constructions and pushouts are the main contributions of this paper and they are compared with the special cases known up to now.


Natural Transformation Graph Transformation Network Graph Local Graph Shared Part 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Hartmut Ehrig
    • 1
  • Fernando Orejas
    • 2
  • Ulrike Prange
    • 1
  1. 1.Technical University of BerlinGermany
  2. 2.Technical University of CataloniaSpain

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