---
_id: '7517'
abstract:
- lang: eng
text: The algebraic approaches to graph transformation are based on the concept
of gluing of graphs, modelled by pushouts in suitable categories of graphs and
graph morphisms. This allows one not only to give an explicit algebraic or set
theoretical description of the constructions, but also to use concepts and results
from category theory in order to build up a rich theory and to give elegant proofs
even in complex situations. In this chapter we start with an overwiev of the basic
notions common to the two algebraic approaches, the double-pushout (DPO) approach
and the singlepushout (SPO) approach; next we present the classical theory and
some recent development of the double-pushout approach. The next chapter is devoted
instead to the single-pushout approach, and it is closed by a comparison between
the two approaches.
author:
- first_name: Andrea
full_name: Corradini, Andrea
last_name: Corradini
- first_name: Ugo
full_name: Montanari, Ugo
last_name: Montanari
- first_name: Francesca
full_name: Rossi, Francesca
last_name: Rossi
- first_name: Hartmut
full_name: Ehrig, Hartmut
last_name: Ehrig
- first_name: Reiko
full_name: Heckel, Reiko
last_name: Heckel
- first_name: Michael
full_name: Löwe, Michael
last_name: Löwe
citation:
ama: 'Corradini A, Montanari U, Rossi F, Ehrig H, Heckel R, Löwe M. Algebraic Approaches
to Graph Transformation, Part I: Basic Concepts and Double Pushout Approach. In:
Handbook of Graph Grammars and Computing by Graph Transformation, Volume 1:
Foundations. Singapore: World Scientific; 1997:163-245.'
apa: 'Corradini, A., Montanari, U., Rossi, F., Ehrig, H., Heckel, R., & Löwe,
M. (1997). Algebraic Approaches to Graph Transformation, Part I: Basic Concepts
and Double Pushout Approach. In Handbook of Graph Grammars and Computing by
Graph Transformation, Volume 1: Foundations (pp. 163–245). Singapore: World
Scientific.'
bibtex: '@inbook{Corradini_Montanari_Rossi_Ehrig_Heckel_Löwe_1997, place={Singapore},
title={Algebraic Approaches to Graph Transformation, Part I: Basic Concepts and
Double Pushout Approach}, booktitle={Handbook of Graph Grammars and Computing
by Graph Transformation, Volume 1: Foundations}, publisher={World Scientific},
author={Corradini, Andrea and Montanari, Ugo and Rossi, Francesca and Ehrig, Hartmut
and Heckel, Reiko and Löwe, Michael}, year={1997}, pages={163–245} }'
chicago: 'Corradini, Andrea, Ugo Montanari, Francesca Rossi, Hartmut Ehrig, Reiko
Heckel, and Michael Löwe. “Algebraic Approaches to Graph Transformation, Part
I: Basic Concepts and Double Pushout Approach.” In Handbook of Graph Grammars
and Computing by Graph Transformation, Volume 1: Foundations, 163–245. Singapore:
World Scientific, 1997.'
ieee: 'A. Corradini, U. Montanari, F. Rossi, H. Ehrig, R. Heckel, and M. Löwe, “Algebraic
Approaches to Graph Transformation, Part I: Basic Concepts and Double Pushout
Approach,” in Handbook of Graph Grammars and Computing by Graph Transformation,
Volume 1: Foundations, Singapore: World Scientific, 1997, pp. 163–245.'
mla: 'Corradini, Andrea, et al. “Algebraic Approaches to Graph Transformation, Part
I: Basic Concepts and Double Pushout Approach.” Handbook of Graph Grammars
and Computing by Graph Transformation, Volume 1: Foundations, World Scientific,
1997, pp. 163–245.'
short: 'A. Corradini, U. Montanari, F. Rossi, H. Ehrig, R. Heckel, M. Löwe, in:
Handbook of Graph Grammars and Computing by Graph Transformation, Volume 1: Foundations,
World Scientific, Singapore, 1997, pp. 163–245.'
date_created: 2019-02-04T22:48:43Z
date_updated: 2022-01-06T07:03:39Z
department:
- _id: '66'
language:
- iso: eng
page: 163-245
place: Singapore
publication: 'Handbook of Graph Grammars and Computing by Graph Transformation, Volume
1: Foundations'
publisher: World Scientific
status: public
title: 'Algebraic Approaches to Graph Transformation, Part I: Basic Concepts and Double
Pushout Approach'
type: book_chapter
user_id: '52534'
year: '1997'
...