Peripheral logic

For any system of, n, nodes with, e (n), edges that can each affect the value, K_n of each node, there exists a minimum "effort" to achieve an arbitrary K_n for a given node, say n_x, from relatively local nodes, n_(i, j, k, 1i, 2j, 3k...Mi,(M+1)j, (M+2)k) = S (K_n).

So for any node n, there's a K_n, achievable by all sets e (n :i .j.k) in S (K_n), but
min { e (n : i.j.k)} for K_n is the most efficient.

I know that's vague, but I'm not sure in what area this is classified. Thanks.