Journal of Mathematical Chemistry

, Volume 50, Issue 5, pp 1347–1361 | Cite as

On the equivalence of direct mechanisms and structurally minimal pathways

  • Mate Barany
  • Botond BertokEmail author
  • Csanad Imreh
  • L. T. Fan
  • Ferenc Friedler
Original Paper


A reaction-pathway identification procedure has two distinct phases. The first phase enumerates exhaustively the feasible candidate pathways, and the second phase identifies the ultimate feasible pathway or pathways among them. Probably the most efficient way to execute the first phase is to algorithmically generate the networks of feasible candidate pathways from a predefined set of plausible elementary reactions. The available algorithmic methods for this purpose can be roughly grouped into two major classes, one based on graph theory and the other on linear algebra. Both classes of methods consider any chemical reaction system as a network of elementary reactions, thereby implying that the two classes are interrelated. This paper studies the linear algebraic concept termed direct mechanism introduced in the mid-eighties and the graph-theoretical concept termed structurally minimal pathway introduced two decades later. Herein, it has been formally proven that the two concepts are equivalent.


Pathway Mechanism Linear algebra Graph theory 


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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Mate Barany
    • 1
  • Botond Bertok
    • 1
    Email author
  • Csanad Imreh
    • 2
  • L. T. Fan
    • 3
  • Ferenc Friedler
    • 1
  1. 1.Department of Computer Science and Systems TechnologyUniversity of PannoniaVeszprémHungary
  2. 2.Department of Computer Algorithms and Artifical IntelligenceUniversity of SzegedSzegedHungary
  3. 3.Department of Chemical EngineeringKansas State UniversityManhattanUSA

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