الگوریتم ادمون

${\displaystyle BV\leftarrow BE\leftarrow \varnothing }$

i=0


A:
if ${\displaystyle BV=V_i}$
 then goto B
for some vertex ${\displaystyle v\notin BV}$
 and ${\displaystyle v\in V_i}$
 {
   ${\displaystyle BV\leftarrow BV\cup \{v\}}$

   find an edge ${\displaystyle e=(x,v)}$
 such that w(e) = max{ w(y,v)|(y,v) ${\displaystyle \in }$
 Ei}
   if w(e) ≤ 0 then goto A
}
if ${\displaystyle BE\cup \{e\}}$
 contains a circuit {
   i=i+1
   construct ${\displaystyle G_i}$
 by shrinking ${\displaystyle C_i}$
 to ${\displaystyle u_i}$

   modify BE, BV and some edge weights
}
${\displaystyle BE\leftarrow BE\cup e}$

goto A


B:
while i ≠ 0 {
   reconstruct ${\displaystyle G_{i-1}}$
 and rename some edges in BE
   if ${\displaystyle u_i}$
 was a root of an out-tree in BE {
       ${\displaystyle BE\leftarrow BE\cup \{e|e\in C_i}$
 and ${\displaystyle e\ne e_0^i\}}$

   }else{
       ${\displaystyle BE\leftarrow BE\cup \{e|e\in C_i}$
 and ${\displaystyle e\ne {\tilde{e}}_i\}}$

   }
   i=i-1
}
Maximum branching weight = ${\displaystyle \sum _{e\in BE}w(e)}$