http://code.activestate.com/recipes/tags/directed/top/2013-04-03T19:30:32-07:00ActiveState Code Recipes2013-04-03T19:30:32-07:00Mark Dickinsonhttp://code.activestate.com/recipes/users/4172683/http://code.activestate.com/recipes/578507-strongly-connected-components-of-a-directed-graph/

<p style="color: grey"> Python recipe 578507 by <a href="/recipes/users/4172683/">Mark Dickinson</a> (<a href="/recipes/tags/connected/">connected</a>, <a href="/recipes/tags/directed/">directed</a>, <a href="/recipes/tags/graph/">graph</a>, <a href="/recipes/tags/strong/">strong</a>, <a href="/recipes/tags/tarjan/">tarjan</a>). Revision 3. </p> <p>Two linear-time algorithms for finding the strongly connected components of a directed graph. <code>strongly_connected_components_tree</code> implements (a variant of) Tarjan's well-known algorithm for finding strongly connected components, while <code>strongly_connected_components_path</code> implements a path-based algorithm due (in this form) to Gabow.</p> <p>Edit: I added an iterative function <code>strongly_connected_components_iterative</code>; this is a direct conversion of <code>strongly_connected_components_path</code> into iterative form. It's therefore safe to use on high-depth graphs, without risk of running into Python's recursion limit.</p>

2011-04-21T13:40:32-07:00jimmy2timeshttp://code.activestate.com/recipes/users/4177690/http://code.activestate.com/recipes/577668-simple-graph-algorithms-with-a-modular-design/

<p style="color: grey"> Python recipe 577668 by <a href="/recipes/users/4177690/">jimmy2times</a> (<a href="/recipes/tags/algorithms/">algorithms</a>, <a href="/recipes/tags/breadth/">breadth</a>, <a href="/recipes/tags/depth/">depth</a>, <a href="/recipes/tags/directed/">directed</a>, <a href="/recipes/tags/first/">first</a>, <a href="/recipes/tags/graph/">graph</a>, <a href="/recipes/tags/object/">object</a>, <a href="/recipes/tags/oriented/">oriented</a>, <a href="/recipes/tags/python/">python</a>, <a href="/recipes/tags/search/">search</a>, <a href="/recipes/tags/theory/">theory</a>, <a href="/recipes/tags/undirected/">undirected</a>, <a href="/recipes/tags/visit/">visit</a>). Revision 7. </p> <p>The purpose of this recipe is to look at algorithmic graph theory from an object-oriented perspective.</p> <p>A graph is built on top of a dictionary indexed by its vertices, each item being the set of neighbours of the key vertex. This ensures that iterating through the neighbours of a vertex is still efficient in sparse graphs (as with adjacency lists) while at the same time checking for adjacency is expected constant-time (as with the adjacency matrix).</p> <p>Any valid class of graph must implement the interface defined by AbstractGraph.</p> <p>A generic search algorithm takes as input a graph, source and target vertices and a queue. A queue must implement the methods Q.get(), Q.put() and Q.empty() in such a way to get the desired order in visiting the vertices.</p> <p>Given this pattern, breadth-first and depth-first search are essentially defined by the corresponding expansion policies: the first one uses an actual FIFO queue, the second one a LIFO queue (or stack).</p>