Erving's Theorem is a result in the field of graph theory, specifically concerning the properties of directed graphs. It states that for any directed graph, there exists a way to assign weights to its edges such that the total weight of incoming edges equals the total weight of outgoing edges for every vertex. This balance is crucial for various applications, including network flow problems. The theorem is named after Herbert Erving, who contributed to the understanding of flow networks and their mathematical properties. It provides a foundational principle for analyzing systems where resources or information flow in multiple directions, ensuring equilibrium at each point in the network.