def copy(self):
G = self.__class__()
# copy the minimum set of properties to get an operative graph copy
G.vertices = set(self.vertices)
G.edges = set_copy(self.edges)
G.neighbors = dict_copy(self.neighbors)
G.first_v = self.first_v
G.v_id = count(self.v_id.next() - 1)
self.v_id = count(self.v_id.next() - 2)
G.identities = dict_copy(self.identities)
G.false_edges = set_copy(self.false_edges)
return G
def random_connected_graph(n, m):
""" Return the random connected graph G_{n,m}.
Gives a graph picked randomly out of the set of all graphs
with n nodes and m edges.
Parameters
----------
n : int
The number of nodes.
m : int
The number of edges.
"""
G = Graph()
V = G + n # add n vertices
max_edges = int((n * (n - 1.0)) / 2.0)
m = min(m, max_edges)
# add the first connection line, (n-1) edges, assuring a connected graph
for u, v in pairwise(V):
G.add_edge(u, v)
AddEdge = G.add_edge
E_star = set_copy(combinations(G.vertices, 2))
for u, v in random.sample(E_star - G.edges, m - n + 1):
AddEdge(u, v)
return G
