I want to build a time expanded graph with time discretization Dt that starts at t = 0 and ends at t = T where between the node (n1, t) and the node (n2, t') is an arc if and only if (n1, n2) were connected in the original graph.

How can this be implemented in pseudo-code? The problem I'm stuck on is how to pass from the original graph to the time expanded one.

(I use C++ and Boost libraries to write the code)