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This work is the first in a series of papers devoted to constructing tablesof structure constants for the complex simple Lie algebras and to finding anexplicit form of Chevalley commutator formulas.  The work consists of three parts. In the first part, expressions are foundfor the structure constants of the complex simple Lie algebra of type F_4 inthe form of functions of structure constants corresponding to extraspecialpairs of roots. As a consequence, all Chevalley commutator formulas[x_r(u),x_s(y)] are calculated when the sum r+s is a root.  Further, in the second part, tables of structure constants and Chevalleycommutator formulas are given in the special case when all constantscorresponding to extraspecial pairs are equal to one.  Finally, in the third part, directed and weighted graphs associated with rootsystems are constructed. It is shown that the elements of the exponent of theadjacency matrices of directed graphs are the numbers P_{rs}, where P_{rs} isthe number of representations of the root r in the form of a sum of the root sand fundamental roots such that any initial segment of the sum is a root. It isalso shown that the elements of an exponent of the weight matrix of a weightedgraph are the values of sums arising when calculating complex commutators inChevalley groups.

The Table of the Structure Constants for the Complex Simple Lie Algebra  of Type F_4 and its Application to the Calculation of Commutators in the  Chevalley Group of Type F_4 over Fields and Rings