# Source code for graphs

```
"""Directed graph algorithm implementations."""
[docs]def creates_cycle(connections, test):
"""
Returns true if the addition of the 'test' connection would create a cycle,
assuming that no cycle already exists in the graph represented by 'connections'.
"""
i, o = test
if i == o:
return True
visited = {o}
while True:
num_added = 0
for a, b in connections:
if a in visited and b not in visited:
if b == i:
return True
visited.add(b)
num_added += 1
if num_added == 0:
return False
[docs]def required_for_output(inputs, outputs, connections):
"""
Collect the nodes whose state is required to compute the final network output(s).
:param inputs: list of the input identifiers
:param outputs: list of the output node identifiers
:param connections: list of (input, output) connections in the network.
NOTE: It is assumed that the input identifier set and the node identifier set are disjoint.
By convention, the output node ids are always the same as the output index.
Returns a set of identifiers of required nodes.
"""
required = set(outputs)
s = set(outputs)
while 1:
# Find nodes not in S whose output is consumed by a node in s.
t = set(a for (a, b) in connections if b in s and a not in s)
if not t:
break
layer_nodes = set(x for x in t if x not in inputs)
if not layer_nodes:
break
required = required.union(layer_nodes)
s = s.union(t)
return required
[docs]def feed_forward_layers(inputs, outputs, connections):
"""
Collect the layers whose members can be evaluated in parallel in a feed-forward network.
:param inputs: list of the network input nodes
:param outputs: list of the output node identifiers
:param connections: list of (input, output) connections in the network.
Returns a list of layers, with each layer consisting of a set of node identifiers.
Note that the returned layers do not contain nodes whose output is ultimately
never used to compute the final network output.
"""
required = required_for_output(inputs, outputs, connections)
layers = []
s = set(inputs)
while 1:
# Find candidate nodes c for the next layer. These nodes should connect
# a node in s to a node not in s.
c = set(b for (a, b) in connections if a in s and b not in s)
# Keep only the used nodes whose entire input set is contained in s.
t = set()
for n in c:
if n in required and all(a in s for (a, b) in connections if b == n):
t.add(n)
if not t:
break
layers.append(t)
s = s.union(t)
return layers
```