A flow_dire_graph F is a directed graph such that:

 Any node v of F has an associated function "balance(v)" such that Sum_v[balance(v)] = 0:
 if (balance(v) > 0) v "supplies" flow;
 if (balance(v) < 0) v "demands" flow;
 if (balance(v) = 0) v "manteins" flow.
 Any edge e of F has associated the following functions:
 lower_cap(e) >= 0;
 upper_cap(e) >= lower_cap(e);
 cost(e);
 flow(e):
 lower_cap(e) <= flow(e) <= upper_cap(e);
 Sum_v[flow(v,w)]  Sum_u[flow(u,v)] = balance(v) for each node v in F.
Definition: We call "cost" of F the following: Sum_e[cost(e)*flow(e)].
NOTE: all the above mathematical functions are considered integral
(that is with integer values only)
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