I was usually using if-then constraints with integer variables but ended up using continuous variables and got confused. I have variables $x_{ij}\in\mathbb{R}_{\geq 0}$, and would like to force the program: if $x_{ij}>0$, then $x_{ji}=0$, where $i,j\in\mathcal{I}$. When I use the following (in which $\mathbb{M}$ is a big number), it looks like the constraint serves to the purpose.
$$x_{ij}\geq \mathbb{M}x_{ji} \qquad \forall i,j\in\mathcal{I}.$$
However, it does a bit further than what is expected and undesired, which is $x_{ji}=0$, when $x_{ij}=0$. The symmetry of this will be conflicting. My variable essentially denotes a flow amount from node $i$ to node $j$, and I would like to ensure: if flow occurs from $i$ to $j$, it should not occur from $j$ to $i$. Thanks in advance!