A graph is a pair $G = (V,E)$ where $E\subseteq V\times V$ is symmetric and irreflexive. The former means that $(x,y)\in E$ iff $(y,x)\in E$ while the later means that $(x,x)\not\in E$ for every $x\in V$. In such case, we say the graph is undirected. Without the assumption of symmetry, we say that a graph is directed. My question is: in the case of a directed graph, every edge $e\in E$ is oriented or it is allowable to have oriented and unoriented edges?
Any help is appreciated.
Generally in a directed Graph every edge is oriented. However depending on the application you could model an un-oriented edge $(x,y)$ by using two oriented edges namely $(x,y)$ and $(y,x)$.