Let G = ( V , E ) be a graph with vertex set V and edge set E . A vertex v ∈ V v e -dominates every edge incident to it as well as every edge adjacent to these incident edges. The vertex–edge degree of a vertex v is the number of edges v e -dominated by v . Similarly, an edge e = u v e v -dominates the two vertices u and v incident to it, as well as every vertex adjacent to u or v . The edge–vertex degree of an edge e is the number of vertices e v -dominated by edge e . In this paper we introduce these types of degrees and study their properties.