highways, etc.) and it contains a fixed number of vehicles; in short it is a conservative network. Pictorially we represent the network by a digraph, as shown in Fig. \[fig01\],

![[]{data-label="fig01"}](Digrafosistfechado.jpg){height="2.4in" width="3.0in"}

where each *loop*, associated with a *vertex*, corresponds to a site that accommodates a certain number of vehicles, whereas each *edge* is a link between the vertices that contains a number of vehicles in transit from one site to the other along the direction of the arrows. To the digraph of Fig. \[fig01\] one associates the array shown in Table \[A0\],

               –               $A$           $B$           $C$           $D$           Sum of the lines entries
  ---------------------------- ------------- ------------- ------------- ------------- --------------------------
              $A$              $R_{1}$       $P_{1}$       $P_{5}$       $Q_{4}$       
              $B$              $Q_{1}$       $R_{2}$       $P_{2}$       $P_{6}$       
              $C$              $Q_{5}$       $Q_{2}$       $R_{3}$       $P_{3}$       
              $D$              $P_{4}$       $Q_{6}$       $Q_{3}$       $R_{4}$       
   Sum of the columns entries  ${\ T}_{1}$   ${\ T}_{2}$   ${\ T}_{3}$   ${\ T}_{4}$   
               –                                                                       

  : []{data-label="A0"}

the sum of the entries of each row, $U_{i}$, and the sum of the entries of each column, $T_{i}$, are presented in Table \[A0\], and in the last row one finds the sums for the total number of vehicles $Y$ in the network.

The core of the array of Table \[A0\] is a $4\times 4$ 