Interval Cliques

We have $N$ intervals $I_1, I_2, ..., I_N$ where $I_j = [L_j, R_j]$ meaning it contains all real numbers between $L_j$ and $R_j$. It is guaranteed that all $2 \cdot N$ endpoints of the intervals are distinct. Construct a graph of $N$ nodes such that there is an edge between nodes $X$ and $Y$ if and only if the following 2 conditions are **both** satisfied : - There exists at least one real numbe