def is_eulerian(graph):
""" Returns True if the graph is Eulerian. """
if graph.is_directed():
if is_connected(graph):
return all((
graph.in_degree(node) == graph.out_degree(node)
for node in graph))
else:
if is_connected(graph):
return all((
graph.degree(node) % 2 == 0
for node in graph))
return False
def is_tree(graph):
''' Returns whether graph is a tree.
This implementation only allows
undirected graphs! '''
if is_connected(graph):
if graph.order() == graph.size() + 1:
return True
return False
def is_bipartite(graph):
''' If graph is bipartite, returns two sets
of nodes U and V, such that every edge
is from a node in U to node in V. If not,
returns None. Graph must be connected! '''
if not is_connected(graph):
return None
start = next(graph.__iter__())
black, red = True, False
color = {start: black}
stack = deque([start])
while stack:
u = stack.pop()
for v in graph[u]:
if v not in color:
color[v] = not color[u]
stack.append(v)
elif color[v] == color[u]:
return None
sets = _groupby(lambda x: color[x], color)
return (sets[black], sets[red])
