Two operations of merging and splitting components in a chain graph

Milan Studený; Alberto Roverato; Šárka Štěpánová

Kybernetika (2009)

  • Volume: 45, Issue: 2, page 208-248
  • ISSN: 0023-5954

Abstract

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In this paper we study two operations of merging components in a chain graph, which appear to be elementary operations yielding an equivalent graph in the respective sense. At first, we recall basic results on the operation of feasible merging components, which is related to classic LWF (Lauritzen, Wermuth and Frydenberg) Markov equivalence of chain graphs. These results are used to get a graphical characterisation of factorisation equivalence of classic chain graphs. As another example of the use of this operation, we derive some important invariants of LWF Markov equivalence of chain graphs. Last, we recall analogous basic results on the operation of legal merging components. This operation is related to the so-called strong equivalence of chain graphs, which includes both classic LWF equivalence and alternative AMP (Andersson, Madigan and Perlman) Markov equivalence.

How to cite

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Studený, Milan, Roverato, Alberto, and Štěpánová, Šárka. "Two operations of merging and splitting components in a chain graph." Kybernetika 45.2 (2009): 208-248. <http://eudml.org/doc/37732>.

@article{Studený2009,
abstract = {In this paper we study two operations of merging components in a chain graph, which appear to be elementary operations yielding an equivalent graph in the respective sense. At first, we recall basic results on the operation of feasible merging components, which is related to classic LWF (Lauritzen, Wermuth and Frydenberg) Markov equivalence of chain graphs. These results are used to get a graphical characterisation of factorisation equivalence of classic chain graphs. As another example of the use of this operation, we derive some important invariants of LWF Markov equivalence of chain graphs. Last, we recall analogous basic results on the operation of legal merging components. This operation is related to the so-called strong equivalence of chain graphs, which includes both classic LWF equivalence and alternative AMP (Andersson, Madigan and Perlman) Markov equivalence.},
author = {Studený, Milan, Roverato, Alberto, Štěpánová, Šárka},
journal = {Kybernetika},
keywords = {chain graph; essential graph; factorisation equivalence; feasible merging components; legal merging components; strong equivalence; essential graph; factorisation equivalence; feasible merging components; legal merging components; strong equivalence},
language = {eng},
number = {2},
pages = {208-248},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Two operations of merging and splitting components in a chain graph},
url = {http://eudml.org/doc/37732},
volume = {45},
year = {2009},
}

TY - JOUR
AU - Studený, Milan
AU - Roverato, Alberto
AU - Štěpánová, Šárka
TI - Two operations of merging and splitting components in a chain graph
JO - Kybernetika
PY - 2009
PB - Institute of Information Theory and Automation AS CR
VL - 45
IS - 2
SP - 208
EP - 248
AB - In this paper we study two operations of merging components in a chain graph, which appear to be elementary operations yielding an equivalent graph in the respective sense. At first, we recall basic results on the operation of feasible merging components, which is related to classic LWF (Lauritzen, Wermuth and Frydenberg) Markov equivalence of chain graphs. These results are used to get a graphical characterisation of factorisation equivalence of classic chain graphs. As another example of the use of this operation, we derive some important invariants of LWF Markov equivalence of chain graphs. Last, we recall analogous basic results on the operation of legal merging components. This operation is related to the so-called strong equivalence of chain graphs, which includes both classic LWF equivalence and alternative AMP (Andersson, Madigan and Perlman) Markov equivalence.
LA - eng
KW - chain graph; essential graph; factorisation equivalence; feasible merging components; legal merging components; strong equivalence; essential graph; factorisation equivalence; feasible merging components; legal merging components; strong equivalence
UR - http://eudml.org/doc/37732
ER -

References

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