The differential on operator S(Γ).

Consider a simple graph $ \Gamma = (V(\Gamma), E(\Gamma)) $ with $ n $ vertices and $ m $ edges. Let $ P $ be a subset of $ V(\Gamma) $ and $ B(P) $ the set of neighbors of $ P $ in $ V(\Gamma)\backslash P $. In the study of graphs, the concept of refers to a measure of how much the number of edges leaving a set of vertices exceeds the size of that set.