def strongly_connected_components(graph):
"""
Tarjan's Algorithm (named for its discoverer, Robert Tarjan) is a graph theory algorithm
for finding the strongly connected components of a graph.
Based on: http://en.wikipedia.org/wiki/Tarjan%27s_strongly_connected_components_algorithm
"""
index_counter = [0]
stack = []
lowlinks = {}
index = {}
result = []
def strongconnect(node):
# set the depth index for this node to the smallest unused index
index[node] = index_counter[0]
lowlinks[node] = index_counter[0]
index_counter[0] += 1
stack.append(node)
# Consider successors of `node`
try:
successors = graph[node]
except:
successors = []
for successor in successors:
if successor not in lowlinks:
# Successor has not yet been visited; recurse on it
strongconnect(successor)
lowlinks[node] = min(lowlinks[node],lowlinks[successor])
elif successor in stack:
# the successor is in the stack and hence in the current strongly connected component (SCC)
lowlinks[node] = min(lowlinks[node],index[successor])
# If `node` is a root node, pop the stack and generate an SCC
if lowlinks[node] == index[node]:
connected_component = []
while True:
successor = stack.pop()
connected_component.append(successor)
if successor == node: break
component = tuple(connected_component)
# storing the result
result.append(component)
for node in graph:
if node not in lowlinks:
strongconnect(node)
return result