Volpert Graph

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In reaction network theory, the Volpert graph plays a very important role. As an abstract idea of reaction kinetics, it is a directed bipartite graph. The vertex set contains the chemical components and the reaction steps, which are the two disjoint classes of the graph. There is an edge between a component and a reaction if and only if the reactant complex contains the component; otherwise, there is an edge between a reaction and a component if and only if the product complex contains the component.
Contributed by: Attila Nagy (March 2011)
Open content licensed under CC BY-NC-SA
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Details
The Volpert graph of the formal reaction mechanism is the following directed bipartite graph:
, where the vertex set
is the set
, and
iff
, and
iff
, where
and
. There is no directed edge inside
nor
.
For more information about the formal reaction mechanism see the "Descriptive Reaction Kinetics" Demonstration.
P. Érdi and J. Tóth, Mathematical Models of Chemical Reactions: Theory and Applications of Deterministic and Stochastic Models, Manchester: Manchester University Press, 1989.
Permanent Citation
"Volpert Graph"
http://demonstrations.wolfram.com/VolpertGraph/
Wolfram Demonstrations Project
Published: March 7 2011