I have a huge directed graph with about a million nodes and more than ten million edges. The edges are not weighted. The graph is a small-world like graph. In fact I see that every node is (on average) connected to another node over three intermediate nodes.
Given this graph can you think of a fast algorithm that returns all paths (without cycles) between a start and a destination node, but only up to a given maximum number N of intermediate nodes (and in my case N most of the time will be between 0 and 3)?
If your graph was undirected, you would certainly want to do a bidirectional breadth first search. For length 2 paths, enumerate edges from the start node and the end node and see where they intersect. For the length 3 paths, go 2 deep from the end point with smaller degree, and one deep on the node with greater degree.
Since your graph is directed, you might want to also keep reverse edges so you can do the same trick.