algorithm - Graph serialization

Question

I'm looking for a simple algorithm to 'serialize' a directed graph. In particular I've got a set of files with interdependencies on their execution order, and I want to find the correct order at compile time. I know it must be a fairly common thing to do - compilers do it all the time - but my google-fu has been weak today. What's the 'go-to' algorithm for this?

Answer 1

Topological Sort (From Wikipedia):

In graph theory, a topological sort or topological ordering of a directed acyclic graph (DAG) is a linear ordering of its nodes in which each node comes before all nodes to which it has outbound edges. Every DAG has one or more topological sorts.

Pseudo code:

L ← Empty list where we put the sorted elements
Q ← Set of all nodes with no incoming edges
while Q is non-empty do
    remove a node n from Q
    insert n into L
    for each node m with an edge e from n to m do
        remove edge e from the graph
        if m has no other incoming edges then
            insert m into Q
if graph has edges then
    output error message (graph has a cycle)
else 
    output message (proposed topologically sorted order: L)