def find_mincycle(graph):
# size = graph.size()
# mincycle = []
# mincycle.append(np.inf)
# matr = graph.to_matrix()
# dist = graph.to_matrix()
# for i in range(size):
# for j in range(size):
# if matr[i][j] == 0:
# matr[i][j] = dist[i][j] = np.inf
# for k in range(size):
# for i in range(k):
# for j in range(i):
# mincycle[0] = min(mincycle[0], dist[i][j] + matr[j][k] + matr[k][i])
#
# for i in range(size):
# for j in range(i):
# temp = dist[i][k] + dist[k][j]
# if temp < dist[i][j]:
# dist[i][j] = dist[j][i] = temp
# if graph.oriented:
# mincycle -= 1
g = nx.Graph()
nx.Graph()
size = graph.size()
matr = graph.to_matrix()
for i in range(1, size + 1):
g.add_node(i)
for j in range(1, size + 1):
if matr[i - 1][j - 1] is not 0:
g.add_edge(i, j)
return nx.minimum_cycle_basis(g)[0]
def task_b(G):
gr = nx.Graph(G)
print("|E| = " + str(gr.number_of_edges()))
print("|V| = " + str(gr.number_of_nodes()))
min = 100
max = -100
gr = maximum_connected_component(gr)
for i in gr.nodes:
if gr.degree[i] < min:
min = gr.degree[i]
if gr.degree[i] > max:
max = gr.degree[i]
print("𝛿(G) = " + str(min))
print("Δ(G) = " + str(max))
print("rad(G) = " + str(nx.radius(gr)))
print("diam(G) = " + str(nx.diameter(gr)))
print("girth(G) = " + str(len(nx.minimum_cycle_basis(G)[0])) + ", " + str(nx.minimum_cycle_basis(G)[0]))
print("center(G) = " + str(nx.center(gr)))
print("𝜅(G) = " + str(nx.node_connectivity(gr)))
print("𝜆(G) = " + str(nx.edge_connectivity(gr)))
def get_cycle_descriptors(graph):
"""Get descriptors for the cycles in a graph"""
cycles = nx.minimum_cycle_basis(graph)
lengths = count_sublist_lengths(cycles)
memberships = get_cycle_memberships(graph, cycles, lengths)
return {
"cycles": cycles,
"lengths": lengths,
"memberships": memberships,
}
def __init__(self, graph):
"""
this is the schema for molecule with fused rings
:param graph:
"""
super().__init__(graph)
self.rings = nx.minimum_cycle_basis(self.graph) # technically sssr
self.rings = sorted(self.rings, key=lambda x: len(x))
self.nrings = len(self.rings)
if self.nrings < 1:
warnings.warn('you are init a MolGraph with no ring!')
self.ring_graph = nx.Graph()
for ij in itertools.combinations(range(self.nrings), 2):
i, j = ij
ri = self.rings[i]
rj = self.rings[j]
shared_nodes = set(ri) & set(rj)
ni_connected_to_rj = [
ni for ni in ri
if len(set(self.graph.neighbors(ni))
& set(rj)) == 1 and ni not in rj
]
# we set len(shared_nodes) > 0 to avoid breaking spiro bicycle
if len(shared_nodes) > 0 or len(ni_connected_to_rj) > 0:
self.ring_graph.add_edge(i,
j,
nshare=len(shared_nodes),
nconnect=len(ni_connected_to_rj))
self.connected_rings = self.get_rings(
'nconnect', 1) # for rubrene len(self.connected_rings[0]) == 8
self.fused_rings = self.get_rings(
'nshare', 2) # for rubrene len(self.fused_rings[0]) == 4
# notice if two rings share2 then they must connect1
try:
self.lgcr = self.connected_rings[0]
except IndexError:
try:
self.lgcr = [self.rings[0]]
except IndexError:
raise GraphError('no rings in the MolGraph!')
try:
self.lgfr = self.fused_rings[0]
except IndexError:
try:
self.lgfr = [self.rings[0]]
except IndexError:
raise GraphError('no rings in the MolGraph!')
def test_cycle_length(self):
g = HypergraphGrammar.load('hyper_grammar.pickle')
for r in g.rules:
if r is not None:
g = r.to_nx()
cycles = nx.minimum_cycle_basis(g)
if len(cycles) > 0:
maxlen = max([len(c) for c in cycles])
if maxlen > 7:
print(maxlen)
cc = nx.number_connected_components(g)
if cc > 1:
print(cc)
def solve_b(G):
Graph = nx.Graph(G)
print("|V| = " + str(len(Graph.nodes)))
print("|E| = " + str(len(Graph.edges)))
Graph = biggest_component(G)
max_degree = -1
min_degree = 1000
for ISO in Graph.nodes:
if Graph.degree[ISO] > max_degree:
max_degree = Graph.degree[ISO]
if Graph.degree[ISO] < min_degree:
min_degree = Graph.degree[ISO]
print("Min deg = " + str(min_degree))
print("Max deg = " + str(max_degree))
print("Radius = " + str(nx.radius(Graph)))
print("Diameter = " + str(nx.diameter(Graph)))
print("Girth = " + str(len(nx.minimum_cycle_basis(G)[0])) + ". Example: " +
str(nx.minimum_cycle_basis(G)[0]))
print("Center: " + str(nx.center(Graph)))
print("Edge connectivity = " + str(nx.edge_connectivity(Graph)))
print("Node connectivity = " + str(nx.node_connectivity(Graph)))
def _find_bonds_and_rings(self, qm_out):
"""Setup networkx graph """
self.graph = nx.Graph()
for i_idx, i_elem in enumerate(self.elements):
self.graph.add_node(i_idx,
elem=i_elem,
n_bonds=qm_out.n_bonds[i_idx],
q=qm_out.point_charges[i_idx],
lone_e=qm_out.lone_e[i_idx],
coords=self.coords[i_idx])
# add bonds
for j_idx, j_elem in enumerate(self.elements):
b_order = qm_out.b_orders[i_idx, j_idx]
if b_order > 0.3:
id1, id2 = sorted([i_elem, j_elem])
b_order_half_rounded = np.round(b_order * 2) / 2
vec = self.coords[i_idx] - self.coords[j_idx]
dist = np.sqrt((vec**2).sum())
self.graph.add_edge(
i_idx,
j_idx,
vector=vec,
length=dist,
order=b_order,
type=f'{id1}({b_order_half_rounded}){id2}',
n_rings=0)
if qm_out.n_bonds[i_idx] > ELE_MAXB[i_elem]:
print(
f"WARNING: Atom {i_idx+1} ({ATOM_SYM[i_elem]}) has too many",
" ({qm_out.n_bonds[i_idx]}) bonds?")
elif qm_out.n_bonds[i_idx] == 0:
print(
f"WARNING: Atom {i_idx+1} ({ATOM_SYM[i_elem]}) has no bonds"
)
# add rings
self.rings = nx.minimum_cycle_basis(self.graph)
self.rings3 = [r for r in self.rings if len(r) == 3]
for i in range(self.n_atoms):
self.node(i)['n_ring'] = sum([i in ring for ring in self.rings])
#
for atoms in self.graph.edges:
ring_members = [
set(atoms).issubset(set(ring)) for ring in self.rings
]
self.edge(*atoms)['n_rings'] = sum(ring_members)
self.edge(*atoms)['in_ring'] = any(ring_members)
self.edge(*atoms)['in_ring3'] = any(
set(atoms).issubset(set(ring)) for ring in self.rings3)
def __init__(self, graph: nx.Graph, joints: dict, partition_scheme: str):
"""
fragment is a BasicGraph with joints
I feel it's not necessary to add parent BasicGraph as an attribute, but I maybe wrong
:param graph:
:param joints: a dict, keys are nodes in the subgraph that have parent graph edges not in this subgraph
"""
super().__init__(graph)
self.partition_scheme = partition_scheme
self.graph = graph
self.joints = joints
self.rings = nx.minimum_cycle_basis(self.graph) # technically sssr
self.rings = sorted(self.rings, key=lambda x: len(x))
def getCycles(graph, grid):
cycles = nx.minimum_cycle_basis(graph)
finalCycles = [cycles[0]]
append = True
for i in range(len(cycles)):
append = True
for j in range(len(finalCycles)):
if (intersection(cycles[i], finalCycles[j]) != []):
append = False
if (append and cycles[i] not in finalCycles):
finalCycles.append(cycles[i])
finalCycles = [
rearangeCycle(finalCycles[i], grid) for i in range(len(finalCycles))
]
return finalCycles
def get_cycle_basis(self, minimum=True):
"""
A wrapper for networkx cycle basis finder
:param minimum: True (default), if minimum cycle basis is sought
:param nxG: networkX graph
:return: list of edge lists, such as [[(0, 1), (1, 2), (2, 3)]...]
or []
and the number of self-loops discarded in the conversion from multi-graph to graph
"""
if self.multigraph:
G, N = self.convert_multigraph_to_graph()
else:
G = self.nxGraph
N = 0
# A list of cycle lists. Each cycle list is a list of nodes which forms a cycle (loop) in G.
# The nodes are not necessarily returned in a order by which they appear in the cycle...
if minimum:
basis = nx.minimum_cycle_basis(G)
else:
basis = nx.cycle_basis(G)
# convert into edge lists...
edge_lists = []
for node_list in basis:
edges = []
start = node_list[0]
p = start
node_list.remove(p)
while node_list:
p_neighbors = {nbor for a, nbor in G.edges(p)}
for q in p_neighbors:
if q in node_list:
# edge between p and q
edges.append((p, q))
node_list.remove(q)
p = q
break
edges.append((p, start)) # return to origin
edge_lists.append(edges)
return edge_lists, N
def cycles(self, calculate_every=1, exclude_zeros=False):
cycles_number = []
cycles_mean_length = []
for reactions in list(self.reactions.values()):
print('.', end='')
self._reset_graph()
cycles_number.append([])
cycles_mean_length.append([])
i = 0
for reaction in reactions:
node1 = (reaction[0], reaction[2])
node2 = (reaction[1], reaction[3])
self.G.add_edge(node1, node2)
if i % calculate_every != 0:
i += 1
continue
i += 1
cycles = nx.minimum_cycle_basis(self.G)
number = len(cycles)
mean_length = 0
if number > 0:
mean_length = sum(len(x) for x in cycles) / float(number)
cycles_number[-1].append(number)
cycles_mean_length[-1].append(mean_length)
print('')
self.cycles_number = np.array(cycles_number)
self.cycles_mean_length = np.array(cycles_mean_length)
# mean_number_ave = np.mean(number_ave_data, axis=0)
# mean_weight_ave = np.mean(weight_ave_data, axis=0)
mean_cycles_number = self._mean(cycles_number)
mean_cycles_mean_length = self._mean(cycles_mean_length,
exclude_zeros=True)
self.topology_data["cycles_number"] = mean_cycles_number
self.topology_data["cycles_mean_length"] = mean_cycles_mean_length
def compute_bonds(structures, molecules):
out_name = []
out_a0 = []
out_a1 = []
out_n = []
out_dist = []
out_error = []
out_type = []
cycle_name = []
cycle_index = []
cycle_seq = []
cycle_atom_index = []
charge_name = []
charge_atom_index = []
charge_value = []
for imol, name in tqdm(list(enumerate(molecules))):
molecule = structures.loc[name]
error = 0
atoms = molecule.atom.values
atoms_idx = molecule.atom_index.values
n_avail = np.asarray([VALENCE_STD[a] for a in atoms])
n_charge = np.zeros(len(atoms), dtype=np.float16)
isleaf = np.zeros(
len(atoms),
dtype=np.bool) # is the atom in the leafs of connection tree?
coords = molecule[['x', 'y', 'z']].values
kdt = KDTree(
coords) # use an optimized structure for closest match query
nbond = {}
connected = {i: {} for i in atoms_idx}
# select Hydrogen first to avoid butadyne-like ordering failures (molecule_name=dsgdb9nsd_000023)
ordered_atoms_index = list(atoms_idx)
ordered_atoms_index.sort(key=lambda i: BOND_ORDER[atoms[i]])
ordered_atoms_index = np.asarray(ordered_atoms_index)
# STEP 1: 1-bond connect each atom with closest match
# only one bond for each atom pair is done in step 1
for a0 in ordered_atoms_index:
search_bonds(kdt,
n_avail,
nbond,
connected,
isleaf,
coords,
atoms,
atoms_idx,
a0,
connect_once=True,
VALENCE=VALENCE_STD)
# STEP 2: greedy connect n-bonds, progressing from leafs of connection tree
while (((n_avail > 0).sum() > 0) and isleaf).sum() > 0:
progress = False
for a0 in ordered_atoms_index:
#print("leaF/Trunk & avail: " + ", ".join([f"{i}:{atoms[i]}={leaflabel[leaf[i]]}{n_avail[i]}"
# for i in ordered_atoms_index]))
if (n_avail[a0] > 0) and isleaf[a0]:
for a1 in connected[a0]:
if (n_avail[a0] > 0) and (n_avail[a1] > 0):
add_bond(n_avail, nbond, a0, a1)
progress = True
if (n_avail[a0] == 0) or (n_avail[a1] == 0):
isleaf[a0] = 1
isleaf[a1] = 1
if not progress:
break
# gather remaining multiple bonds
if n_avail.sum() > 0:
for key in nbond.keys():
a0, a1 = key
while (n_avail[a0] > 0) and (n_avail[a1] > 0):
add_bond(n_avail, nbond, a0, a1)
# STEP 3: search for known ionized radicals
if n_avail.sum() > 0:
for (i, a) in zip(atoms_idx, atoms):
if a == 'N':
# NH3+
bonded_str, bonded_idx = get_bonded_atoms(atoms, nbond, i)
if (bonded_str == "HHH") and (n_avail[i] == 0):
# add a valence unit and search a dangling bond nearby
n_avail[i] += 1
n_charge[i] += 1
if search_bonds(kdt,
n_avail,
nbond,
connected,
isleaf,
coords,
atoms,
atoms_idx,
i,
connect_once=False,
VALENCE=VALENCE_MAX):
print(f"++ NH3+ found for {name} atom_index={i}")
else:
print(
f"** NH3+ bonding failure for {name} atom_index={i}"
)
elif (a == 'O') and (n_avail[i] == 1):
# COO-
bonded_str, bonded_idx = get_bonded_atoms(atoms, nbond, i)
if bonded_str == "C":
C_i = bonded_idx[0]
C_bonded_str, C_bonded_idx = get_bonded_atoms(
atoms, nbond, C_i)
if ("OO" in C_bonded_str):
has_2CO = False
#print (C_bonded_str, C_bonded_idx, nbond, name)
for a1, i1 in zip(C_bonded_str, C_bonded_idx):
key = tuple(sorted((C_i, i1)))
if (a1 == 'O') and (nbond[key][0] == 2):
has_2CO = True
if (len(C_bonded_idx) == 3) and has_2CO:
# found carboxyle!
n_avail[i] -= 1
print(
f"** COO- found for {name} C_atom_index={C_i}"
)
for a1, i1 in zip(C_bonded_str, C_bonded_idx):
if a1 == 'O':
n_charge[i1] = -0.5
key = tuple(sorted((C_i, i1)))
nbond[key][0] = 1.5
# detect cycles : algo complexity in O(m^2 * n)
# paper : https://link.springer.com/article/10.1007/s00453-007-9064-z
# nx doc: https://networkx.github.io/documentation/latest/reference/algorithms/generated/networkx.algorithms.cycles.minimum_cycle_basis.html
graph = nx.Graph([bond for bond in nbond.keys()])
unordered_cycles = nx.minimum_cycle_basis(graph)
# index atoms by their sequential order in the cycle: i.e follow bonds
# Note: this code can be written in a much cleaner way!
if len(unordered_cycles) > 0:
for icycle, c in enumerate(unordered_cycles):
available = {i: 1 for i in c}
a0 = c[0]
cycle = [a0]
del (available[a0])
for index in range(1, len(c)):
# get atoms bonded to a0
bonded = [b for b in nbond.keys() if a0 in b]
bonded = list(
map(lambda b: b[0] if b[1] == a0 else b[1], bonded))
# get next atom and remove it from cycle
assert (len(bonded) > 0)
found = False
for a1 in bonded:
if (a1 in bonded) and (a1 in available):
cycle.append(a1)
del (available[a1])
a0 = a1
found = True
break
assert (found)
# and add cycles found to the cycle dataframe lists
cycle_name.extend([name] * len(cycle))
cycle_index.extend([icycle] * len(cycle))
cycle_seq.extend(np.arange(len(cycle)))
cycle_atom_index.extend(cycle)
# display info on failed molecules
if n_avail.sum() > 0:
error = 1
print(
f" Remaining bondings={n_avail.sum()} for molecule_name={name}, atoms: "
+ ", ".join(
[f"{i}:{atoms[i]}" for i in atoms_idx if n_avail[i] > 0]))
# inputs for DataFrame bonds
for (a0, a1), (n, dist) in nbond.items():
# append to python lists which is 7x faster than toa pd.DataFrame
out_name.append(name)
out_a0.append(a0)
out_a1.append(a1)
out_n.append(n)
out_dist.append(dist)
out_error.append(error)
out_type.append(f"{n:0.1f}" +
"".join(sorted(f"{atoms[a0]}{atoms[a1]}")))
# inputs for DataFrame charges
charge_name.extend([name] * len(atoms))
charge_atom_index.extend(molecule.atom_index.values)
charge_value.extend(n_charge)
bonds = pd.DataFrame({
'molecule_name': out_name,
'atom_index_0': out_a0,
'atom_index_1': out_a1,
'nbond': out_n,
'L2dist': out_dist,
'error': out_error,
'bond_type': out_type
})
charges = pd.DataFrame({
'molecule_name': charge_name,
'atom_index': charge_atom_index,
'charge': charge_value
})
cycles = pd.DataFrame({
'molecule_name': cycle_name,
'cycle_index': cycle_index,
'cycle_seq': cycle_seq,
'atom_index': cycle_atom_index
})
return bonds, charges, cycles
def calculate(graph):
if nx.is_connected(graph):
return len(nx.minimum_cycle_basis(graph))
else:
return 10**10
def make_graph(self):
"""Generate edge information to create a graph
Using the intersection of each face, create edge information that makes up the face
Args:
self.new_line_info: List of aligned floor points
self.new_line_info2: List of aligned intersections points
Returns:
new_edges: List of edge information
pointcloud_i: Index information of PointCloud including each surface
"""
ceiling, floor, wall = [], [], []
self.make_line_info()
if len(self.index_value) > 0:
G = nx.Graph()
# Making the graph using index_value list
G.add_edges_from(self.index_value)
# Finding the minimum cycle from the Graph
cycles_list = nx.minimum_cycle_basis(G)
if len(cycles_list) >= 1:
delete_edges = []
temp_delete = []
# Finding the overlapping edges between generated cycles
for each_cycle in cycles_list:
# First making original edge information the each cycles node and self.index_value
# eahc_cycle is not sorted
for each_cycle_i in range(len(each_cycle) - 1):
for each_edge in self.index_value:
if each_cycle[each_cycle_i] in each_edge:
index_node = each_edge.index(
each_cycle[each_cycle_i])
for each_cycle_j in range(
each_cycle_i + 1, len(each_cycle)):
if each_cycle[each_cycle_j] in each_edge:
if index_node == 0:
temp_edge = [
each_cycle[each_cycle_i],
each_cycle[each_cycle_j]
]
else:
temp_edge = [
each_cycle[each_cycle_j],
each_cycle[each_cycle_i]
]
temp_delete.append(temp_edge)
delete_dup_edges = list(set(map(tuple, temp_delete)))
if len(delete_dup_edges) > 0:
for delete_edge in delete_dup_edges:
# Second checking the duplicate edges
if temp_delete.count([delete_edge[0], delete_edge[1]
]) > 1:
delete_edges.append(
[delete_edge[0], delete_edge[1]])
# After removing the duplicate edges, finding all cycles included from the Graph
if len(delete_edges) > 0:
G.remove_edges_from(delete_edges)
new_cycles = nx.minimum_cycle_basis(G)
ceiling, floor, wall = self.get_newGraph(G, new_cycles)
else:
ceiling, floor, wall = self.get_newGraph(G, cycles_list)
return ceiling, floor, wall
g=np.ndarray.tolist(gnp)
tr1=numTriangles(g)
# print(tr1)
len_trlist=len(tr1)
if(len_trlist==0):
print("triangles removed from graph")
else:
continue
if(nx.is_connected(graph)==False):
print("removing triangles causes disconnection!")
continue
# cycl_list=nx.cycle_basis(graph, 0)
cycl_list=nx.minimum_cycle_basis(graph)
if(len(cycl_list)):
# girthObtained=len(min(cycl_list, key=len))
girthObtained=len(cycl_list[0])
girthCycle=cycl_list[0]
# girthCycle=min(cycl_list, key=len)
print("girth = "+str(girthObtained))
else:
print("no cycles")
continue
if (girthObtained!=girth):
print("girth doesn't match")
continue
else:
def __create_loop_relationships__(G, initial_cycle_weight, cycle_weight,
edge_attribute):
"""
helper function to determine child parent relationship for loops (or any other structural components)
Input
networkx graph G
edge_attribute str, the name of the edge weight to be considered for type cycle
cycle_weight
the weight based on which edge are removed
max: edge with the highest edge weight
min: edge with the lowest edge weight
betweenness_max: edge with the highest betweenness value
betweenness_min: edge with the lowest betweenness value
initial_cycle_weight
if true then the initial cycle basis is estimated based on edge weight
with https://networkx.github.io/documentation/stable/reference/algorithms/generated/networkx.algorithms.cycles.minimum_cycle_basis.html#networkx.algorithms.cycles.minimum_cycle_basis
else the initial cycles are estimated based on steps only
with https://networkx.github.io/documentation/stable/reference/algorithms/generated/networkx.algorithms.cycles.cycle_basis.html#networkx.algorithms.cycles.cycle_basis
Output
dict of final loops
dict of relationships
dict of all loops
"""
if initial_cycle_weight:
cycles = nx.minimum_cycle_basis(G)
else:
cycles = nx.cycle_basis(G)
#print("cycles", cycles)
#convert cycles into dict & edge list
cycles_dict = __convert_cycles__(cycles)
#print("cycles", cycles_dict)
#construct dict to save cycles and give them id which is saved in tree
#append each new created loop to dict
save_loops = {}
all_loops = {}
for i in range(len(cycles_dict)):
all_loops[i] = cycles_dict[i]
save_loops[i] = cycles_dict[i]
#2nd dict that stores loop id and child nodes in list
#initialize leave nodes
relationship = {}
for loop in all_loops:
relationship[loop] = [None, None]
#merged cycles - stores cycles already merged
merged_nodes = []
print("start creating hierarchical tree")
while len(G.edges()) > 0:
#community weight functions are used to find the most valuable edge
if cycle_weight == "max":
to_remove = __by_weight__(G, w_max=True, attribute=edge_attribute)
elif cycle_weight == "min":
to_remove = __by_weight__(G, w_max=False, attribute=edge_attribute)
elif cycle_weight == "betweenness_max":
to_remove = __by_centrality__(G,
w_max=True,
attribute=edge_attribute,
type="betweenness")
elif cycle_weight == "betweenness_min":
to_remove = __by_centrality__(G,
w_max=False,
attribute=edge_attribute,
type="betweenness")
else:
print("cycle weight not known, please select another one")
return None
break
#remove edge from graph
G.remove_edge(to_remove[0], to_remove[1])
children = []
cycle = []
for loop_ID, loop in all_loops.items():
#compare edges (independent of direction (x,y) == (y,x))
#print(loop)
#print(to_remove)
if ((to_remove in loop) or ((to_remove[1], to_remove[0]) in loop)):
children.append(loop_ID)
merged_nodes.append(loop_ID)
#new cycle is made up of all child edges except the removed edge
for edge in loop:
if ((edge not in cycle)
and ((edge[1], edge[0]) not in cycle)):
if edge != to_remove and edge != (to_remove[1],
to_remove[0]):
cycle.append(edge)
new_key = int(sorted(save_loops.keys())[-1]) + 1
all_loops[new_key] = cycle
save_loops[new_key] = cycle
#and remove merged loops
for child in children:
del all_loops[child]
#add parent child connection to relationship
new_stage = int(sorted(relationship.keys())[-1]) + 1
#find ID of children
relationship[new_key] = children
print("finished edge removal")
return all_loops, relationship, save_loops
from bmpga.utils.io_utils import XYZReader
reader = XYZReader()
XYZs = glob("test_data/*.xyz")
print(XYZs)
for xyz in XYZs:
print(xyz)
cluster = reader.read(xyz, return_clusters=True)[0]
print(cluster.molecules)
graph = cluster.molecules[0].to_graph()
nodes = graph.nodes
for node in nodes:
print(node.__dict__)
print(graph.nodes)
print(graph.edges)
cycles = nx.cycle_basis(graph)
print(cycles)
print(len(cycles))
print(nx.minimum_cycle_basis(graph))
def get_cycle_lengths(graph):
"""Get the length of cycles in a graph"""
cycles = nx.minimum_cycle_basis(graph)
lengths = count_sublist_lengths(cycles)
return lengths