def generate(num_nodes, num_edges, directed=False, weight_range=(1, 1)):
"""
Create a random graph.
@type num_nodes: number
@param num_nodes: Number of nodes.
@type num_edges: number
@param num_edges: Number of edges.
@type directed: bool
@param directed: Whether the generated graph should be directed or not.
@type weight_range: tuple
@param weight_range: tuple of two integers as lower and upper limits on randomly generated
weights (uniform distribution).
"""
# Graph creation
if directed:
random_graph = digraph()
else:
random_graph = graph()
# Nodes
nodes = range(num_nodes)
random_graph.add_nodes(nodes)
# Build a list of all possible edges
edges = []
edges_append = edges.append
for x in nodes:
for y in nodes:
if ((directed and x != y) or (x > y)):
edges_append((x, y))
# Randomize the list
shuffle(edges)
# Add edges to the graph
min_wt = min(weight_range)
max_wt = max(weight_range)
for i in range(num_edges):
each = edges[i]
random_graph.add_edge((each[0], each[1]), wt = randint(min_wt, max_wt))
return random_graph
def cut_tree(igraph, caps = None):
"""
Construct a Gomory-Hu cut tree by applying the algorithm of Gusfield.
@type igraph: graph
@param igraph: Graph
@type caps: dictionary
@param caps: Dictionary specifying a maximum capacity for each edge. If not given, the weight of the edge
will be used as its capacity. Otherwise, for each edge (a,b), caps[(a,b)] should be given.
@rtype: dictionary
@return: Gomory-Hu cut tree as a dictionary, where each edge is associated with its weight
"""
#maximum flow needs a digraph, we get a graph
#I think this conversion relies on implementation details outside the api and may break in the future
graph = digraph()
graph.add_graph(igraph)
#handle optional argument
if not caps:
caps = {}
for edge in graph.edges():
caps[edge] = igraph.edge_weight(edge)
#temporary flow variable
f = {}
#we use a numbering of the nodes for easier handling
n = {}
N = 0
for node in graph.nodes():
n[N] = node
N = N + 1
#predecessor function
p = {}.fromkeys(range(N),0)
p[0] = None
for s in range(1,N):
t = p[s]
S = []
#max flow calculation
(flow,cut) = maximum_flow(graph,n[s],n[t],caps)
for i in range(N):
if cut[n[i]] == 0:
S.append(i)
value = cut_value(graph,flow,cut)
f[s] = value
for i in range(N):
if i == s:
continue
if i in S and p[i] == t:
p[i] = s
if p[t] in S:
p[s] = p[t]
p[t] = s
f[s] = f[t]
f[t] = value
#cut tree is a dictionary, where each edge is associated with its weight
b = {}
for i in range(1,N):
b[(n[i],n[p[i]])] = f[i]
return b