depth-first search:
follows paths as far as it can
start at a node
visit its first (unvisited) neighbor
visit the neighbor's first (unvisited) neighbor
and so on
visit the first neighbor's next (unvisited) neighbor

cycle detection

topological sort of directed acyclic graph via dfs
what's a topological sort?
  ordering of vertices such that v is after u if (u,v) is an edge in the
  graph
pick a vertex
  do dfs
  remember which nodes were visited
  pick an unvisited node
  do dfs, finding any new unvisited nodes, append result to
    previous search
  repeat until all nodes found