def relation_to_span(g1, g2, relation, edges=False, attrs=False):
"""Convert a relation to a span."""
new_graph = type(g1)()
left_h = dict()
right_h = dict()
for a, bs in relation.items():
for b in bs:
new_node = str(a) + "_" + str(b)
new_graph.add_node(new_node)
if attrs:
common_attrs = attrs_intersection(g1.get_node(a),
g2.get_node(b))
new_graph.add_node_attrs(new_node, common_attrs)
left_h[new_node] = a
right_h[new_node] = b
for n1 in new_graph.nodes():
for n2 in new_graph.nodes():
if (left_h[n1], left_h[n2]) in g1.edges() and\
(right_h[n1], right_h[n2]) in g2.edges():
new_graph.add_edge(n1, n2)
common_attrs = attrs_intersection(
g1.get_edge(left_h[n1], left_h[n2]),
g2.get_edge(right_h[n1], right_h[n2]),
)
new_graph.add_edge_attrs(n1, n2, common_attrs)
return new_graph, left_h, right_h
def relation_to_span(g1,
g2,
relation,
edges=False,
attrs=False,
directed=True):
"""Convert a relation to a span."""
if directed:
new_graph = nx.DiGraph()
else:
new_graph = nx.Graph()
left_h = dict()
right_h = dict()
for a, b in relation:
new_node = str(a) + "_" + str(b)
new_graph.add_node(new_node)
if attrs:
common_attrs = attrs_intersection(g1.node[a], g2.node[b])
add_node_attrs(new_graph, new_node, common_attrs)
left_h[new_node] = a
right_h[new_node] = b
for n1 in new_graph.nodes():
for n2 in new_graph.nodes():
if (left_h[n1], left_h[n2]) in g1.edges() and\
(right_h[n1], right_h[n2]) in g2.edges():
new_graph.add_edge(n1, n2)
common_attrs = attrs_intersection(
g1.edge[left_h[n1]][left_h[n2]],
g2.edge[right_h[n1]][right_h[n2]],
)
add_edge_attrs(new_graph, n1, n2, common_attrs)
return (new_graph, left_h, right_h)
def relation_to_span(g1, g2, relation, edges=False, attrs=False, directed=True):
"""Convert a relation to a span."""
if directed:
new_graph = nx.DiGraph()
else:
new_graph = nx.Graph()
left_h = dict()
right_h = dict()
for a, bs in relation.items():
for b in bs:
new_node = str(a) + "_" + str(b)
new_graph.add_node(new_node)
if attrs:
common_attrs = attrs_intersection(
g1.node[a],
g2.node[b]
)
add_node_attrs(new_graph, new_node, common_attrs)
left_h[new_node] = a
right_h[new_node] = b
for n1 in new_graph.nodes():
for n2 in new_graph.nodes():
if (left_h[n1], left_h[n2]) in g1.edges() and\
(right_h[n1], right_h[n2]) in g2.edges():
new_graph.add_edge(n1, n2)
common_attrs = attrs_intersection(
g1.adj[left_h[n1]][left_h[n2]],
g2.adj[right_h[n1]][right_h[n2]],
)
add_edge_attrs(
new_graph,
n1, n2,
common_attrs
)
return new_graph, left_h, right_h
def get_rule_projections(tx, hierarchy, graph_id, rule, instance, rhs_typing=None):
"""Execute the query finding rule liftings."""
if rhs_typing is None:
rhs_typing = {}
projections = {}
if rule.is_relaxing():
if len(rule.lhs.nodes()) > 0:
lhs_instance = {
n: instance[n] for n in rule.lhs.nodes()
}
lhs_vars = {
n: n for n in rule.lhs.nodes()}
match_instance_vars = {
v: lhs_instance[k] for k, v in lhs_vars.items()
}
# Match nodes
query = "// Match nodes the instance of the rewritten graph \n"
query += "MATCH {}".format(
", ".join([
"({}:{} {{id: '{}'}})".format(k, graph_id, v)
for k, v in match_instance_vars.items()
])
)
query += "\n\n"
carry_vars = list(lhs_vars.values())
for k, v in lhs_vars.items():
query += (
"OPTIONAL MATCH (n)<-[:typing*1..]-({})\n".format(v) +
"WITH {} \n".format(
", ".join(
carry_vars +
["collect(DISTINCT {{type:'node', origin: {}.id, id: n.id, graph:labels(n)[0], attrs: properties(n)}}) as {}_dict\n".format(
v, v)])
)
)
carry_vars.append("{}_dict".format(v))
# Match edges
for (u, v) in rule.p.edges():
edge_var = "{}_{}".format(lhs_vars[u], lhs_vars[v])
query += "OPTIONAL MATCH ({}_instance)-[{}:edge]->({}_instance)\n".format(
lhs_vars[u],
edge_var,
lhs_vars[v])
query += "WHERE ({})<-[:typing*1..]-({}) AND ({})<-[:typing*1..]-({})\n".format(
"{}_instance".format(lhs_vars[u]), lhs_vars[u],
"{}_instance".format(lhs_vars[v]), lhs_vars[v])
query += (
"WITH {} \n".format(
", ".join(carry_vars + [
"collect({{type: 'edge', source: {}.id, target: {}.id, graph:labels({})[0], attrs: properties({})}}) as {}\n".format(
"{}_instance".format(lhs_vars[u]),
"{}_instance".format(lhs_vars[v]),
"{}_instance".format(lhs_vars[u]),
edge_var,
edge_var)
])
)
)
carry_vars.append(edge_var)
query += "RETURN {}".format(
", ".join(
["{}_dict as {}".format(v, v) for v in lhs_vars.values()] +
["{}_{}".format(lhs_vars[u], lhs_vars[v]) for u, v in rule.p.edges()]))
result = tx.run(query)
record = result.single()
l_l_ts = {}
l_nodes = {}
l_edges = {}
for k, v in record.items():
if len(v) > 0:
if v[0]["type"] == "node":
for el in v:
l_node = keys_by_value(instance, el["origin"])[0]
if el["graph"] not in l_nodes:
l_nodes[el["graph"]] = {}
l_l_ts[el["graph"]] = {}
if el["id"] not in l_nodes[el["graph"]]:
l_nodes[el["graph"]][el["id"]] = {}
l_nodes[el["graph"]][el["id"]] = attrs_union(
l_nodes[el["graph"]][el["id"]],
attrs_intersection(
generic.convert_props_to_attrs(el["attrs"]),
get_node(rule.lhs, l_node)))
l_l_ts[el["graph"]][l_node] = el["id"]
else:
for el in v:
l_sources = keys_by_value(l_l_ts[el["graph"]], el["source"])
l_targets = keys_by_value(l_l_ts[el["graph"]], el["target"])
for l_source in l_sources:
for l_target in l_targets:
if exists_edge(rule.l, l_source, l_target):
if el["graph"] not in l_edges:
l_edges[el["graph"]] = {}
if (el["source"], el["target"]) not in l_edges[el["graph"]]:
l_edges[el["graph"]][(el["source"], el["target"])] = {}
l_edges[el["graph"]][(el["source"], el["target"])] =\
attrs_union(
l_edges[el["graph"]][(el["source"], el["target"])],
attrs_intersection(
generic.convert_props_to_attrs(el["attrs"]),
get_edge(rule.lhs, l_source, l_target)))
for graph, typing in hierarchy.get_descendants(graph_id).items():
if graph in l_nodes:
nodes = l_nodes[graph]
else:
nodes = {}
if graph in l_edges:
edges = l_edges[graph]
else:
edges = {}
l = nx.DiGraph()
add_nodes_from(l, [(k, v) for k, v in nodes.items()])
if graph in l_edges:
add_edges_from(
l,
[(s, t, v) for (s, t), v in edges.items()])
rhs, p_rhs, r_r_t = pushout(
rule.p, l, rule.rhs, compose(rule.p_lhs, l_l_ts[graph]), rule.p_rhs)
l_t_t = {n: n for n in nodes}
# Modify P_T and R_T according to the controlling
# relation rhs_typing
if graph in rhs_typing.keys():
r_t_factorization = {
r_r_t[k]: v
for k, v in rhs_typing[graph].items()
}
added_t_nodes = set()
for n in rhs.nodes():
if n in r_t_factorization.keys():
# If corresponding R_T node is specified in
# the controlling relation add nodes of T
# that type it to P
t_nodes = r_t_factorization[n]
for t_node in t_nodes:
if t_node not in l_t_t.values() and\
t_node not in added_t_nodes:
new_p_node = generate_new_id(
l.nodes(), t_node)
l.add_node(new_p_node)
added_t_nodes.add(t_node)
p_rhs[new_p_node] = n
l_t_t[new_p_node] = t_node
else:
p_rhs[keys_by_value(l_t_t, t_node)[0]] = n
projections[graph] = {
"rule": Rule(p=l, rhs=rhs, p_rhs=p_rhs),
"instance": l_t_t,
"l_l_t": l_l_ts[graph],
"p_p_t": {k: l_l_ts[graph][v] for k, v in rule.p_lhs.items()},
"r_r_t": r_r_t
}
return projections
def get_rule_liftings(tx, graph_id, rule, instance, p_typing=None):
"""Execute the query finding rule liftings."""
if p_typing is None:
p_typing = {}
liftings = {}
if len(rule.lhs.nodes()) > 0:
lhs_vars = {
n: n for n in rule.lhs.nodes()}
match_instance_vars = {lhs_vars[k]: v for k, v in instance.items()}
# Match nodes
query = "// Match nodes the instance of the rewritten graph \n"
query += "MATCH {}".format(
", ".join([
"({}:{} {{id: '{}'}})".format(k, graph_id, v)
for k, v in match_instance_vars.items()
])
)
query += "\n\n"
carry_vars = list(lhs_vars.values())
for k, v in lhs_vars.items():
query += (
"OPTIONAL MATCH (n)-[:typing*1..]->({})\n".format(v) +
"WITH {} \n".format(
", ".join(carry_vars + [
"collect({{type:'node', origin: {}.id, id: n.id, graph:labels(n)[0], attrs: properties(n)}}) as {}_dict\n".format(
v, v)])
)
)
carry_vars.append("{}_dict".format(v))
# Match edges
for (u, v) in rule.lhs.edges():
edge_var = "{}_{}".format(lhs_vars[u], lhs_vars[v])
query += "OPTIONAL MATCH ({}_instance)-[{}:edge]->({}_instance)\n".format(
lhs_vars[u],
edge_var,
lhs_vars[v])
query += "WHERE ({})-[:typing*1..]->({}) AND ({})-[:typing*1..]->({})\n".format(
"{}_instance".format(lhs_vars[u]), lhs_vars[u],
"{}_instance".format(lhs_vars[v]), lhs_vars[v])
query += (
"WITH {} \n".format(
", ".join(carry_vars + [
"collect({{type: 'edge', source: {}.id, target: {}.id, attrs: properties({}), graph:labels({})[0]}}) as {}\n".format(
"{}_instance".format(lhs_vars[u]),
"{}_instance".format(lhs_vars[v]),
edge_var,
"{}_instance".format(lhs_vars[u]),
edge_var)
])
)
)
carry_vars.append(edge_var)
query += "RETURN {}".format(
", ".join(
["{}_dict as {}".format(v, v) for v in lhs_vars.values()] +
["{}_{}".format(lhs_vars[u], lhs_vars[v]) for u, v in rule.lhs.edges()]))
result = tx.run(query)
record = result.single()
l_g_ls = {}
lhs_nodes = {}
lhs_edges = {}
for k, v in record.items():
if len(v) > 0:
if v[0]["type"] == "node":
for el in v:
if el["graph"] not in lhs_nodes:
lhs_nodes[el["graph"]] = []
l_g_ls[el["graph"]] = {}
l_g_ls[el["graph"]][el["id"]] = keys_by_value(
instance, el["origin"])[0]
# compute attr intersection
attrs = attrs_intersection(
generic.convert_props_to_attrs(el["attrs"]),
get_node(rule.lhs, l_g_ls[el["graph"]][el["id"]]))
lhs_nodes[el["graph"]].append((el["id"], attrs))
else:
for el in v:
if el["graph"] not in lhs_edges:
lhs_edges[el["graph"]] = []
# compute attr intersection
attrs = attrs_intersection(
generic.convert_props_to_attrs(el["attrs"]),
get_edge(
rule.lhs,
l_g_ls[el["graph"]][el["source"]],
l_g_ls[el["graph"]][el["target"]]))
lhs_edges[el["graph"]].append(
(el["source"], el["target"], attrs)
)
for graph, nodes in lhs_nodes.items():
lhs = nx.DiGraph()
add_nodes_from(lhs, nodes)
if graph in lhs_edges:
add_edges_from(
lhs, lhs_edges[graph])
p, p_lhs, p_g_p = pullback(
lhs, rule.p, rule.lhs, l_g_ls[graph], rule.p_lhs)
l_g_g = {n[0]: n[0] for n in nodes}
# Remove controlled things from P_G
if graph in p_typing.keys():
l_g_factorization = {
keys_by_value(l_g_g, k)[0]: v
for k, v in p_typing[graph].items()
}
p_g_nodes_to_remove = set()
for n in p.nodes():
l_g_node = p_lhs[n]
# If corresponding L_G node is specified in
# the controlling relation, remove all
# the instances of P nodes not mentioned
# in this relations
if l_g_node in l_g_factorization.keys():
p_nodes = l_g_factorization[l_g_node]
if p_g_p[n] not in p_nodes:
del p_g_p[n]
del p_lhs[n]
p_g_nodes_to_remove.add(n)
for n in p_g_nodes_to_remove:
p.remove_node(n)
liftings[graph] = {
"rule": Rule(p=p, lhs=lhs, p_lhs=p_lhs),
"instance": l_g_g,
"l_g_l": l_g_ls[graph],
"p_g_p": p_g_p
}
else:
query = generic.ancestors_query(graph_id, "graph", "homomorphism")
result = tx.run(query)
ancestors = [record["ancestor"] for record in result]
for a in ancestors:
liftings[a] = {
"rule": Rule.identity_rule(),
"instance": {},
"l_g_l": {},
"p_g_p": {}
}
return liftings