Think of the election as a Bus route from source, S, to Target, T. a directed graph G=(V,E), where V is the set of vertices (nodes) and E is the set of edges. Each edge (i,j)∈E has an associated non-negative cost (or length) c_ij

Let x_ij​ be a binary variable that equals 1 if edge (i,j) is included in the shortest path, and 0 otherwise.

Minimize ∑​_(i,j)∈E [c_ij​x_ij​]

Subject to:

∑_j:(s,j)∈E[x_sj]−∑_i:(i,s)∈E [x_is]=1

∑_i:(i,t)∈E [x_it]−∑_j:(t,j)∈E [x_tj]=−1

∑_i:(i,k)∈E [x_ik]−∑_j:(k,j)∈E [x_kj]=0∀k∈V∖{s,t}

x_ij∈{0,1}∀(i,j)∈E