In a directed graph, the imbalance of a vertex v is b(v) = d + (v) - d - (v). We characterize the integer lists that can occur as the sequence of imbalances of a simple directed graph. For the realizable sequences, we determine the maximum number of arcs in a realization and provide a greedy algorithm that constructs realizations with the minimum number of arcs. © 2001 Elsevier Science B.V. All rights reserved.
Mubayi, D., Will, T. G., & West, D. B. (2001). Realizing degree imbalances in directed graphs. Discrete Mathematics, 239(1–3), 147–153. https://doi.org/10.1016/S0012-365X(01)00048-6