In an undirected graph, the degree $d(u)$ of a vertex $u$ is the number of neighbors $u$ has, or equivalently, the number of edges incident upon it. In a directed graph, we distinguish between the indegree $d_{in} (u)$, which is the number of edges into $u$, and the outdegree $d_{out} (u)$, the number of edges leaving $u$.

Source: Algorithms by Dasgupta, Papadimitriou, Vazirani. McGraw-Hill. 2006.