Substantiation of the Mason rule

Let us prove the validity of the Mason rule formulated above [see eqn. (11)] for linear mechanisms with many cycles (routes). 

A set of quasi-steady-state equations for a linear mechanism is of the form 6(e)tf = 0, where x and c are the vector-columns of the concentrations for the intermediates and observed substances (those participating in the brutto-reaction, i.e. initial substances and products) and b(c) is the matrix of the reaction weights 

In addition the law of conservation must be fulfilled for the total amount, C, of intermediates per unit catalyst surface 

In this case we assume the absence of any additional laws of conservation arising in the case when a linear system has autonomous groups of substances (see Sect. 5.1). 

Let eqns. (32) correspond to the graph G according to the following rule every rth intermediate corresponds to a graph node. Let us express it, like the concentration of an intermediate, through x. The nodes xs and xt are joined by the edge (x, xt) if the coefficient bst in eqns. (32) does not equal zero. 

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