A difference labeling of a graph G is an injective function f : V (G) → N ∪ {0} together with the weight function f^∗ on E(G) given by f^∗(uv) = |f(u) - f(v)| for every edge uv in G. The collection of subgraphs induced by the edges of the same weight is a decomposition of G and is called the common weight decomposition of G induced by f. Let ϒ_f denote the collection of all the paths taken from each member of the common weight decomposition induced by f. A difference labeling f of G is said to be a graphoidal difference labeling if ϒ_f is an acyclic graphoidal decomposition of G. This paper initiates a study on this concepts.