Volpert Graph of Chemical Reactions

In reaction network theory, the Volpert graph is a directed bipartite graph whose vertex sets are the chemical species and the reaction steps. There is an edge from a species to a reaction step if and only if the reactant complex of the reaction step contains the species, and there is an edge from a reaction step to a species if and only if the product complex of the reaction step contains the species. The Volpert graph turns out to be very important in theory and it corresponds to the definition of the graphs used by biochemists.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


The Volpert graph of the formal reaction mechanism is the directed bipartite graph: , where the vertex set is the set , and , iff , and , iff , where and . There is no directed edge either inside or inside .
The Demonstration can also be used to analyze any other type of reaction. 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, Princeton: Princeton University Press, 1989.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+