def test_subgraph(graph, subgraph, final_set, subgraph_vertices=None):
"""
Examine whether the planted subgraph pattern was found. For G(k, q), this examination requires knowing the vertices
that belong to the subgraph, otherwise we look for a specific pattern and do not care whether we found exactly the
vertices of the planted subgraph.
"""
if subgraph == "clique":
return all(
[graph.has_edge(v1, v2) for v1, v2 in combinations(final_set, 2)])
elif subgraph == "dag-clique":
return all([
any([graph.has_edge(v1, v2),
graph.has_edge(v2, v1)])
for v1, v2 in combinations(final_set, 2)
] + [
nx.is_directed_acyclic_graph(nx.induced_subgraph(graph, final_set))
])
elif subgraph == "k-plex":
return all([
d[1] >= len(final_set) - 2
for d in nx.degree(nx.induced_subgraph(graph, final_set))
])
elif subgraph == "biclique":
if not nx.is_connected(nx.induced_subgraph(graph, final_set)):
return False
try:
first, second = nx.algorithms.bipartite.basic.sets(
nx.induced_subgraph(graph, final_set))
return all(
[graph.has_edge(v1, v2) for v1, v2 in product(first, second)])
except nx.exception.NetworkXError:
return False
else: # G(k, q). The only case we have the exact vertices we want and not a subgraph shape.
return len(subgraph_vertices) == len(
set(subgraph_vertices).intersection(set(final_set)))
def test_subgraph(graph, subgraph, final_set, subgraph_vertices=None):
if subgraph == "clique":
return all(
[graph.has_edge(v1, v2) for v1, v2 in combinations(final_set, 2)])
elif subgraph == "dag-clique":
return all([
any([graph.has_edge(v1, v2),
graph.has_edge(v2, v1)])
for v1, v2 in combinations(final_set, 2)
] + [
nx.is_directed_acyclic_graph(nx.induced_subgraph(graph, final_set))
])
elif subgraph == "k-plex":
return all([
d[1] >= len(final_set) - 2
for d in nx.degree(nx.induced_subgraph(graph, final_set))
])
elif subgraph == "biclique":
if not nx.is_connected(nx.induced_subgraph(graph, final_set)):
return False
try:
first, second = nx.algorithms.bipartite.basic.sets(
nx.induced_subgraph(graph, final_set))
return all(
[graph.has_edge(v1, v2) for v1, v2 in product(first, second)])
except nx.exception.NetworkXError:
return False
else: # G(k, q). The only case we have the exact vertices we want and not a subgraph shape.
return len(subgraph_vertices) == len(
set(subgraph_vertices).intersection(set(final_set)))
def test_partial_subgraph(self):
G = self.K3
H = nx.induced_subgraph(G, 0)
assert_equal(dict(H.adj), {0: {}})
assert_not_equal(dict(G.adj), {0: {}})
H = nx.induced_subgraph(G, [0, 1])
assert_equal(dict(H.adj), {0: {1: {}}, 1: {0: {}}})
def test_partial_subgraph(self):
G = self.K3
H = nx.induced_subgraph(G, 0)
assert_equal(dict(H.adj), {0: {}})
assert_not_equal(dict(G.adj), {0: {}})
H = nx.induced_subgraph(G, [0, 1])
assert_equal(dict(H.adj), {0: {1: {}}, 1: {0: {}}})
def test_partial_subgraph(self):
G = self.K3
H = nx.induced_subgraph(G, 0)
assert dict(H.adj) == {0: {}}
assert dict(G.adj) != {0: {}}
H = nx.induced_subgraph(G, [0, 1])
assert dict(H.adj) == {0: {1: {}}, 1: {0: {}}}
def R(G, T, e):
T.remove_edges_from([e])
components = list(nx.connected_components(T))
T.add_edges_from([e])
A = components[0]
B = components[1]
G_A = nx.induced_subgraph(G, A)
G_B = nx.induced_subgraph(G, B)
return [G_A, G_B]
def test_subgraph(self):
assert_equal(self.G.subgraph([0, 1, 2, 4]).adj,
nx.subgraph(self.G, [0, 1, 2, 4]).adj)
assert_equal(self.DG.subgraph([0, 1, 2, 4]).adj,
nx.subgraph(self.DG, [0, 1, 2, 4]).adj)
assert_equal(self.G.subgraph([0, 1, 2, 4]).adj,
nx.induced_subgraph(self.G, [0, 1, 2, 4]).adj)
assert_equal(self.DG.subgraph([0, 1, 2, 4]).adj,
nx.induced_subgraph(self.DG, [0, 1, 2, 4]).adj)
# subgraph-subgraph chain is allowed in function interface
H = nx.induced_subgraph(self.G.subgraph([0, 1, 2, 4]), [0, 1, 4])
assert_is_not(H._graph, self.G)
assert_equal(H.adj, self.G.subgraph([0, 1, 4]).adj)
def test_subgraph(self):
assert_equal(self.G.subgraph([0, 1, 2, 4]).adj,
nx.subgraph(self.G, [0, 1, 2, 4]).adj)
assert_equal(self.DG.subgraph([0, 1, 2, 4]).adj,
nx.subgraph(self.DG, [0, 1, 2, 4]).adj)
assert_equal(self.G.subgraph([0, 1, 2, 4]).adj,
nx.induced_subgraph(self.G, [0, 1, 2, 4]).adj)
assert_equal(self.DG.subgraph([0, 1, 2, 4]).adj,
nx.induced_subgraph(self.DG, [0, 1, 2, 4]).adj)
# subgraph-subgraph chain is allowed in function interface
H = nx.induced_subgraph(self.G.subgraph([0, 1, 2, 4]), [0, 1, 4])
assert_is_not(H._graph, self.G)
assert_equal(H.adj, self.G.subgraph([0, 1, 4]).adj)
def test_subgraph(self):
assert (self.G.subgraph([0, 1, 2, 4]).adj ==
nx.subgraph(self.G, [0, 1, 2, 4]).adj)
assert (self.DG.subgraph([0, 1, 2, 4]).adj ==
nx.subgraph(self.DG, [0, 1, 2, 4]).adj)
assert (self.G.subgraph([0, 1, 2, 4]).adj ==
nx.induced_subgraph(self.G, [0, 1, 2, 4]).adj)
assert (self.DG.subgraph([0, 1, 2, 4]).adj ==
nx.induced_subgraph(self.DG, [0, 1, 2, 4]).adj)
# subgraph-subgraph chain is allowed in function interface
H = nx.induced_subgraph(self.G.subgraph([0, 1, 2, 4]), [0, 1, 4])
assert H._graph is not self.G
assert H.adj == self.G.subgraph([0, 1, 4]).adj
def inspect_remainders(test_scores, test_lbs, eval_scores, eval_lbs, train_scores, train_lbs,
graph_size, subgraph_size, graph_indices, key_name, dirname, iteration):
scores = train_scores + eval_scores + test_scores
lbs = train_lbs + eval_lbs + test_lbs
head_path = os.path.join(os.path.dirname(__file__), '..', 'graph_calculations', 'pkl', key_name[0], key_name[1] + '_runs')
if not os.path.exists(os.path.join("remaining_after_model", key_name[0], dirname)):
os.mkdir(os.path.join("remaining_after_model", key_name[0], dirname))
dumping_path = os.path.join("remaining_after_model", key_name[0], dirname, key_name[1] + "_runs")
for run in range(len(graph_indices)):
ranks, labels = map(lambda x: x[run * graph_size:(run + 1) * graph_size], [scores, lbs])
dir_path = os.path.join(head_path, key_name[1] + "_run_" + str(graph_indices[run][1]))
sorted_vertices = np.argsort(ranks)
initial_candidates = sorted_vertices[-2*subgraph_size:]
total_graph = pickle.load(open(os.path.join(dir_path, "gnx.pkl"), "rb"))
induced_subgraph = nx.induced_subgraph(total_graph, initial_candidates)
candidate_scores, candidate_labels = map(lambda x: [x[c] for c in initial_candidates], [ranks, labels])
candidate_dumping_path = os.path.join(dumping_path, key_name[1] + "_run_" + str(graph_indices[run][1]))
if not os.path.exists(candidate_dumping_path):
os.mkdir(candidate_dumping_path)
all_df = pd.DataFrame({"score": ranks, "label": labels}, index=list(range(graph_size)))
all_df = all_graph_measurements(total_graph, induced_subgraph).join(all_df)
all_df.to_csv(os.path.join(candidate_dumping_path,
f"all_results_iteration_{iteration}_set_{graph_indices[run][0]}.csv"))
cand_df = pd.DataFrame({"score": candidate_scores, "label": candidate_labels}, index=initial_candidates)
cand_df = candidate_graph_measurements(total_graph, induced_subgraph, initial_candidates).join(cand_df)
cand_df.to_csv(os.path.join(candidate_dumping_path,
f"candidates_results_iteration_{iteration}_set_{graph_indices[run][0]}.csv"))
def induced_subgraph(
G, filter_type, filter_attribute, filter_values, ignore_attrs=False
):
"""
Create custom induced subgraph.
Args:
filter_type: 'node' or 'edge'
filter_attribute: attribute to filter on
filter_values: attribute values to evaluate to `True`
"""
G = nx.MultiDiGraph(G)
if filter_type == "node":
nodes = [
n for n in G.nodes() if G.nodes[n].get(filter_attribute) in filter_values
]
sG = nx.induced_subgraph(G, nodes)
elif filter_type == "edge":
sG = nx.MultiDiGraph()
sG.add_nodes_from(G.nodes(data=not ignore_attrs))
sG.add_edges_from(
[
(e[0], e[1], e[-1])
for e in G.edges(data=True)
if e[-1][filter_attribute] in filter_values
]
)
else:
raise
sG.graph["name"] = "_".join(
[G.graph["name"], filter_type, filter_attribute, str(*filter_values)]
)
return sG
def rep(g):
nbar = {
u: nx.induced_subgraph(g, [v for v in g if v not in g[u]])
for u in g
}
x = {
u: {v: LpVariable(f'x{u},{v}', cat='Binary')
for v in nbar[u]}
for u in g
}
lp = LpProblem()
lp += lpSum([x[u][u] for u in g])
for v in g:
lp += lpSum([x[u][v] for u in nbar[v]]) >= 1
for u in g:
for v, w in nbar[u].edges:
lp += x[u][v] + x[u][w] <= x[u][u]
lp.writeLP('rep.lp')
PULP_CBC_CMD(msg=0).solve(lp)
reps = [u for u in g if x[u][u].varValue > 0]
cols = [None] * g.order()
for c, v in enumerate(reps):
cols[v] = c
for c, r in enumerate(reps):
for v in [v for v, xi in x[r].items() if xi.varValue > 0]:
if v not in reps:
cols[v] = c
return cols
def intermediate_subgraph(graph, source, target):
paths = nx.all_simple_paths(graph, source, target)
nodes = set()
for path in paths:
for node in path:
nodes.add(node)
return nx.induced_subgraph(graph, nodes)
def _algorithm(self, graph, labels):
# INITIALIZATION - optimal solutions from a version of the paper#
alpha = 0.8
beta = 2.3
eta = 1.2
eps_4 = 1. / alpha - 1e-8
t = eps_4 * np.log(self._params['vertices']) / \
np.log(np.power(self.rho(alpha, beta, eta), 2) / self.tau(alpha, beta))
t = np.floor(t)
v_i = [v for v in range(len(labels))]
# First Stage #
for _ in range(int(t)):
s_i = self._choose_s_i(v_i, alpha)
s_i_tilde = self._get_si_tilde(graph, s_i, eta)
new_vi = self._get_vi(graph, v_i, s_i, s_i_tilde, beta)
v_i = new_vi
# Second Stage #
g_t = nx.induced_subgraph(graph, v_i)
k_tilde = self._get_k_tilde(g_t, alpha, beta, eta, t)
# Third Stage - From K' to K* using the rule they said at the bottom of the paper #
k_tag = self._get_k_tag(k_tilde, graph)
k_star = self._get_k_star(k_tag, graph)
print(
f"After the final stage, {len([v for v in k_star if labels[v]])} clique vertices "
f"out of {len(k_star)} vertices are left")
return [1 if v in k_star else 0 for v in graph]
def test_restricted_induced_subgraph_chains(self):
""" Test subgraph chains that both restrict and show nodes/edges.
A restricted_view subgraph should allow induced subgraphs using
G.subgraph that automagically without a chain (meaning the result
is a subgraph view of the original graph not a subgraph-of-subgraph.
"""
hide_nodes = [3, 4, 5]
hide_edges = [(6, 7)]
RG = nx.restricted_view(self.G, hide_nodes, hide_edges)
nodes = [4, 5, 6, 7, 8]
SG = nx.induced_subgraph(RG, nodes)
SSG = RG.subgraph(nodes)
assert_is(SSG.root_graph, SSG._graph)
assert_is_not(SG.root_graph, SG._graph)
assert_edges_equal(SG.edges, SSG.edges)
# should be same as morphing the graph
CG = self.G.copy()
CG.remove_nodes_from(hide_nodes)
CG.remove_edges_from(hide_edges)
assert_edges_equal(CG.edges(nodes), SSG.edges)
CG.remove_nodes_from([0, 1, 2, 3])
assert_edges_equal(CG.edges, SSG.edges)
# switch order: subgraph first, then restricted view
SSSG = self.G.subgraph(nodes)
RSG = nx.restricted_view(SSSG, hide_nodes, hide_edges)
assert_is_not(RSG.root_graph, RSG._graph)
assert_edges_equal(RSG.edges, CG.edges)
def test_restricted_induced_subgraph_chains(self):
""" Test subgraph chains that both restrict and show nodes/edges.
A restricted_view subgraph should allow induced subgraphs using
G.subgraph that automagically without a chain (meaning the result
is a subgraph view of the original graph not a subgraph-of-subgraph.
"""
hide_nodes = [3, 4, 5]
hide_edges = [(6, 7)]
RG = nx.restricted_view(self.G, hide_nodes, hide_edges)
nodes = [4, 5, 6, 7, 8]
SG = nx.induced_subgraph(RG, nodes)
SSG = RG.subgraph(nodes)
assert RG._graph is self.G
assert SSG._graph is self.G
assert SG._graph is RG
assert_edges_equal(SG.edges, SSG.edges)
# should be same as morphing the graph
CG = self.G.copy()
CG.remove_nodes_from(hide_nodes)
CG.remove_edges_from(hide_edges)
assert_edges_equal(CG.edges(nodes), SSG.edges)
CG.remove_nodes_from([0, 1, 2, 3])
assert_edges_equal(CG.edges, SSG.edges)
# switch order: subgraph first, then restricted view
SSSG = self.G.subgraph(nodes)
RSG = nx.restricted_view(SSSG, hide_nodes, hide_edges)
assert RSG._graph is not self.G
assert_edges_equal(RSG.edges, CG.edges)
def _get_k_star(self, k_tag, graph):
if len(k_tag) <= self.k:
return k_tag
g_k_tag = nx.induced_subgraph(graph, k_tag)
vertices = [v for v in g_k_tag]
degrees = [g_k_tag.degree(v) for v in vertices]
vertices_order = [vertices[v] for v in np.argsort(degrees)]
return vertices_order[-self.k:]
def test_subgraph_of_subgraph(self):
for G in [self.G, self.DG, self.DMG, self.MG]:
SG = nx.induced_subgraph(G, [4, 5, 6])
assert_equal(list(SG), [4, 5, 6])
SSG = SG.subgraph([6, 7])
assert_equal(list(SSG), [6])
# subgraph-subgraph chain is short-cut in base class method
assert_is(SSG._graph, G)
def subtree(self, G, k):
H = copy.deepcopy(G)
path_to_parent = [(j, k) for j in H if G.has_edge(j, k) and j <= k]
H.remove_edges_from(path_to_parent)
conn_comp = nx.connected_components(H)
node = list(filter(lambda x: k in x, conn_comp))[0]
node_sorted = sorted(node)
subtree = nx.induced_subgraph(H, node_sorted)
return subtree
def cut_edges(G, T, e):
T.remove_edges_from([e])
components = list(nx.connected_components(T))
T.add_edges_from([e])
A = components[0]
B = components[1]
G_A = nx.induced_subgraph(G, A)
G_B = nx.induced_subgraph(G, B)
edges_of_G = list(G.edges())
for x in list(G_A.edges()):
if x in edges_of_G:
edges_of_G.remove(x)
if (x[1], x[0]) in edges_of_G:
edges_of_G.remove((x[1], x[0]))
for x in list(G_B.edges()):
if x in edges_of_G:
edges_of_G.remove(x)
if (x[1], x[0]) in edges_of_G:
edges_of_G.remove((x[1], x[0]))
return edges_of_G
def test_subgraph_of_subgraph(self):
SGv = nx.subgraph(self.G, range(3, 7))
SDGv = nx.subgraph(self.DG, range(3, 7))
SMGv = nx.subgraph(self.MG, range(3, 7))
SMDGv = nx.subgraph(self.MDG, range(3, 7))
for G in self.graphs + [SGv, SDGv, SMGv, SMDGv]:
SG = nx.induced_subgraph(G, [4, 5, 6])
assert list(SG) == [4, 5, 6]
SSG = SG.subgraph([6, 7])
assert list(SSG) == [6]
# subgraph-subgraph chain is short-cut in base class method
assert SSG._graph is G
def test_subgraph_of_subgraph(self):
SGv = nx.subgraph(self.G, range(3, 7))
SDGv = nx.subgraph(self.DG, range(3, 7))
SMGv = nx.subgraph(self.MG, range(3, 7))
SMDGv = nx.subgraph(self.MDG, range(3, 7))
for G in self.graphs + [SGv, SDGv, SMGv, SMDGv]:
SG = nx.induced_subgraph(G, [4, 5, 6])
assert_equal(list(SG), [4, 5, 6])
SSG = SG.subgraph([6, 7])
assert_equal(list(SSG), [6])
# subgraph-subgraph chain is short-cut in base class method
assert_is(SSG._graph, G)
def directed_induced_subgraph(graph, source: str, target: str):
"""
Induced subgraph on edges along shortest paths between source
and target. networkx.exception.NetworkXNoPath if no path
"""
try:
shortest_paths = all_shortest_paths(graph, source, target)
edges = edges_on_paths(shortest_paths)
subgraph = graph.edge_subgraph(edges)
except NetworkXNoPath:
raise
if source == target:
subgraph = nx.induced_subgraph(graph, source)
return subgraph
def test_subgraph_order(self):
G = self.G
G_sub = G.subgraph([1, 2, 3])
assert_equals(list(G.nodes), list(G_sub.nodes))
assert_equals(list(G.edges), list(G_sub.edges))
assert_equals(list(G.pred[3]), list(G_sub.pred[3]))
assert_equals([2, 1], list(G_sub.pred[3]))
assert_equals([], list(G_sub.succ[3]))
G_sub = nx.induced_subgraph(G, [1, 2, 3])
assert_equals(list(G.nodes), list(G_sub.nodes))
assert_equals(list(G.edges), list(G_sub.edges))
assert_equals(list(G.pred[3]), list(G_sub.pred[3]))
assert_equals([2, 1], list(G_sub.pred[3]))
assert_equals([], list(G_sub.succ[3]))
def test_subgraph_order(self):
G = self.G
G_sub = G.subgraph([1, 2, 3])
assert list(G.nodes) == list(G_sub.nodes)
assert list(G.edges) == list(G_sub.edges)
assert list(G.pred[3]) == list(G_sub.pred[3])
assert [2, 1] == list(G_sub.pred[3])
assert [] == list(G_sub.succ[3])
G_sub = nx.induced_subgraph(G, [1, 2, 3])
assert list(G.nodes) == list(G_sub.nodes)
assert list(G.edges) == list(G_sub.edges)
assert list(G.pred[3]) == list(G_sub.pred[3])
assert [2, 1] == list(G_sub.pred[3])
assert [] == list(G_sub.succ[3])
def all_license_subgraphs(g, licenses, quota=1, proportion=0):
"""Takes a graph and returns the subgraphs induced by different
licenses types.
Parameters:
g: either a gt.Graph or a nx.Graph
licenses: list of keys to be used for the return dict
quota: an int for the minimum number of licenses of a given type to appear
in that licenses subgraph
proportion: a float for the proportion of licenses on the domain that should
be the given license type
Returns:
a dict mapping string license names to subgraphs
"""
if isinstance(g, gt.Graph):
subgraph_by_license = dict()
for license in licenses:
nodes = g.new_vp('bool')
for v in g.vertices():
cc_licenses = g.vp['cc_licenses'][v]
if isinstance(cc_licenses, dict):
total_licenses = sum(cc_licenses.values())
if (license in cc_licenses and
cc_licenses[license] >= proportion * total_licenses
and cc_licenses[license] >= quota):
nodes[v] = True
else:
nodes[v] = False
subgraph_by_license[license] = gt.GraphView(g, vfilt=nodes)
return subgraph_by_license
elif isinstance(g, nx.Graph):
subgraph_by_license = dict()
for license in licenses:
nodes = set()
for v, data in g.nodes(data=True):
cc_licenses = data['cc_licenses']
if isinstance(cc_licenses, dict):
total_licenses = sum(cc_licenses.values())
if (license in cc_licenses and
cc_licenses[license] >= proportion * total_licenses
and cc_licenses[license] >= quota):
nodes.add(v)
subgraph_by_license[license] = nx.induced_subgraph(g, nodes)
return subgraph_by_license
else:
raise TypeError('graph format not recognized, must be nx or gt')
def measure_paths(row,
vocab,
node_from,
node_to,
avoiding,
avoiding_property=1):
graph = nx.Graph()
def l(j):
return vocab.inverse_lookup(j)
only_using_nodes = [
l(i[0]) for i in row["kb_nodes"] if l(i[avoiding_property]) != avoiding
] + [node_from, node_to]
for i in row["kb_nodes"]:
graph.add_node(l(i[0]), attr_dict={"body": [l(j) for j in i]})
for id_a, connections in enumerate(
row["kb_adjacency"][:row["kb_nodes_len"]]):
for id_b, connected in enumerate(connections[:row["kb_nodes_len"]]):
if connected:
node_a = row["kb_nodes"][id_a]
node_b = row["kb_nodes"][id_b]
edge = (l(node_a[0]), l(node_b[0]))
graph.add_edge(*edge)
induced_subgraph = nx.induced_subgraph(graph, only_using_nodes)
try:
shortest_path_avoiding = len(
nx.shortest_path(induced_subgraph, node_from, node_to)) - 2
except:
shortest_path_avoiding = None
pass
try:
shortest_path = len(nx.shortest_path(graph, node_from, node_to)) - 2
except:
shortest_path = None
pass
return {
"shortest_path": shortest_path,
"shortest_path_avoiding": shortest_path_avoiding,
}
def restrict_graph_by_property(g, prop):
"""Takes a DiGraph and returns the induced subgraph view for nodes that have
the given property.
Parameters:
g: networkx DiGraph
prop: boolean function that takes in (node, data)
Returns:
a networkx subgraph view for the induced subgraph
"""
if not isinstance(g, nx.Graph):
raise TypeError('not a networkx graph')
subgraph_nodes = []
for node_id, data in g.nodes(data=True):
if prop(node_id, data):
subgraph_nodes.append(node_id)
return nx.induced_subgraph(g, subgraph_nodes)
def remove_edges_map(graph,tree,edge_list):
'''This is the map that produces a partition from a tree and a list of edges
:graph: the graph to be partitioned
:tree: a chosen spanning tree on the graph
:edge_list: a list of edges of the tree
returns list of subgraphs induced by the components of the forest
obtained by removing 'edge_list edges from tree
these correspond to the 'districts'
'''
tree.remove_edges_from(edge_list)
components = list(nx.connected_components(tree.to_undirected()))
tree.add_edges_from(edge_list)
subgraphs = [nx.induced_subgraph(graph, subtree) for subtree in components]
#This is expensive - TODO in case of error
return subgraphs
def _parse_loops_from_graph(self, graph):
"""
Return all Loop instances that can be extracted from a graph.
:param graph: The graph to analyze.
:return: A list of all the Loop instances that were found in the graph.
"""
outtop = []
outall = []
for subg in ( networkx.induced_subgraph(graph, nodes).copy() for nodes in networkx.strongly_connected_components(graph)):
if len(subg.nodes()) == 1:
if len(list(subg.successors(list(subg.nodes())[0]))) == 0:
continue
thisloop, allloops = self._parse_loop_graph(subg, graph)
if thisloop is not None:
outall += allloops
outtop.append(thisloop)
return outtop, outall
def main():
""" Reads in a graph and prints an approximate TSP tour """
graph_file_path = sys.argv[1]
input_graph = nx.read_weighted_edgelist(graph_file_path)
# Compute an MST for G
mst = nx.minimum_spanning_tree(input_graph)
# Compute the subgraph in G induced by odd-degree vertices of the MST
# Find a minimum-weight matching in this graph
odd_verts = list(filter(lambda v: mst.degree(v) % 2 == 1, list(mst.nodes)))
odd_induced_graph = nx.induced_subgraph(input_graph, odd_verts).copy()
# Need to flip the edge weights since networkx only has a max-weight matching function
orig_edges = list(odd_induced_graph.edges.items())
max_weight = max(orig_edges,
key=lambda pair: pair[1]['weight'])[1]['weight']
# subtract the max edge weight from every edge
flipped_edges = list(map(lambda pair: \
(pair[0][0], pair[0][1], max_weight - pair[1]['weight']), orig_edges))
odd_induced_graph.add_weighted_edges_from(flipped_edges)
matching = nx.max_weight_matching(odd_induced_graph, maxcardinality=True)
# Union the MST with the matching to get an Eulerian multigraph
# We can forget the weights at this point
augmented_mst = nx.MultiGraph()
augmented_mst.add_edges_from(mst.edges)
augmented_mst.add_edges_from(matching)
# Compute an Eulerian circuit of the augmented MST and shortcut if necessary
tour_nodes = [u for u, v in nx.eulerian_circuit(augmented_mst)]
final_tour = []
for node in tour_nodes:
if node not in final_tour:
final_tour.append(node)
final_tour.append(final_tour[0])
print("Approximate TSP Tour:", final_tour)
def get_connected_subgraphs(self) -> tuple:
""" Generates the set of (weakly) connected components of the object's graph
Returns:
tuple of connected subgraphs of the original processing graph
"""
if not isinstance(self.graph, networkx.Graph):
raise ValueError('Graph must be built before SnowShuGraph can get graphs from it.')
dags = [networkx.induced_subgraph(self.graph, bunch)
for bunch in networkx.weakly_connected_components(self.graph)]
# set the views flag
for dag in dags:
dag.contains_views = False
for relation in dag.nodes:
dag.contains_views = any((dag.contains_views, relation.is_view,))
return tuple(dags)
def children(H_nodes, G):
#returns the list of all children of subgraph H in graph G
#In the tree described in the comments above
N = neighbors(H_nodes, G)
#input H as a list of nodes
admissable_additions = []
for n in N:
H_nodes.add(n)
candidate_child = nx.induced_subgraph(G, H_nodes)
H_nodes.remove(n)
P = parent(candidate_child)
if P == H_nodes:
admissable_additions.append(n)
admissable_children = []
for n in admissable_additions:
H_nodes.add(n)
admissable_children.append(copy.deepcopy(H_nodes))
H_nodes.remove(n)
return admissable_children
def run_dgp(sz, p, sg_sz, subgraph, write=False, writer=None):
"""
An implementation of the algorithm of Dekel, Gurel-Gurevich and Peres for clique recovery
using degree-based measurements.
"""
graphs, all_labels = graphs_loader(sz, p, sg_sz, subgraph)
remaining_subgraph_vertices = []
start_time = time.time()
for graph, labels in zip(graphs, all_labels):
alpha, beta, eta = 0.8, 2.3, 1.2
eps_4 = 1. / alpha - 1e-8
t = eps_4 * np.log(sz) / np.log(
np.power(dgp_rho(alpha, beta, eta, sg_sz / np.sqrt(sz)), 2) /
dgp_tau(alpha, beta))
t = np.floor(t)
v_i = [v for v in range(len(labels))]
# First Stage #
for _ in range(int(t)):
s_i = dgp_choose_s_i(v_i, alpha)
s_i_tilde = dgp_get_si_tilde(graph, s_i, eta)
new_vi = dgp_get_vi(graph, v_i, s_i, s_i_tilde, beta)
v_i = new_vi
# Second Stage #
g_t = nx.induced_subgraph(graph, v_i)
k_tilde = dgp_get_k_tilde(g_t, alpha, beta, eta, t,
sg_sz / np.sqrt(sz), sg_sz)
# INCLUDING the third, extension stage #
k_tag = dgp_get_k_tag(k_tilde, graph)
k_star = dgp_get_k_star(k_tag, graph, sg_sz)
remaining_subgraph_vertices.append(
len([v for v in k_star if labels[v]]))
total_time = time.time() - start_time
if write:
assert writer is not None
writer.writerow([
str(val) for val in
[sz, sg_sz,
np.round(np.mean(remaining_subgraph_vertices), 4)]
])
return total_time, np.mean(remaining_subgraph_vertices)
def test_full_graph(self):
G = self.K3
H = nx.induced_subgraph(G, [0, 1, 2, 5])
assert_equal(H.name, G.name)
self.graphs_equal(H, G)
self.same_attrdict(H, G)
def test_subgraph_toundirected(self):
SG = nx.induced_subgraph(self.G, [4, 5, 6])
SSG = SG.to_undirected()
assert_equal(list(SSG), [4, 5, 6])
assert_equal(sorted(SSG.edges), [(4, 5), (5, 6)])
