[sage-support] Re: graph.trace_faces() gives me inconsistent results
Haha, apologies for screwing up the review process. To continue from the
previous posts, if you first re-order the embedding to actually be clockwise,
then the trace_faces() method works as expected:
import numpy
def reorder_embedding(emb, locs):
new_emb = {}
for i,neighbors in emb.iteritems():
def angle(b):
dx = locs[b][0] - locs[i][0]
dy = locs[b][1] - locs[i][1]
return numpy.arctan2(dx,dy)
reorder_neighbors = sorted(neighbors, key=angle)
new_emb[i] = reorder_neighbors
return new_emb
S = Graph(lat)
S.show(vertex_size = 600, pos = nodes_dict)
S.is_planar(set_embedding = True)
s_emb = S.get_embedding()
s_emb_r = reorder_embedding(s_emb, nodes_dict)
print SAGE embedding:, s_emb
print Reordered:, s_emb_r
faces = S.trace_faces(s_emb)
print SAGE faces:, faces
faces_r = S.trace_faces(s_emb_r)
print Reordered:, faces_r
SAGE embedding: {1: [2], 2: [1, 3, 5], 3: [4, 9, 5, 2], 4: [5, 6, 7, 8, 9, 3],
5: [2, 3, 6, 4], 6: [7, 4, 5], 7: [8, 4, 6], 8: [9, 4, 7], 9: [3, 4, 8]}
Reordered: {1: [2], 2: [3, 5, 1], 3: [9, 4, 5, 2], 4: [9, 8, 7, 6, 5, 3], 5:
[2, 3, 4, 6], 6: [4, 7, 5], 7: [8, 6, 4], 8: [7, 4, 9], 9: [8, 4, 3]}
SAGE faces: [[(6, 4), (4, 7), (7, 6)], [(3, 2), (2, 5), (5, 3)], [(5, 4), (4,
6), (6, 5)], [(7, 8), (8, 9), (9, 3), (3, 5), (5, 6), (6, 7)], [(1, 2), (2, 3),
(3, 4), (4, 5), (5, 2), (2, 1)], [(4, 9), (9, 8), (8, 4)], [(7, 4), (4, 8), (8,
7)], [(3, 9), (9, 4), (4, 3)]]
Reordered: [[(6, 4), (4, 5), (5, 6)], [(4, 7), (7, 8), (8, 4)], [(3, 2), (2,
5), (5, 3)], [(5, 4), (4, 3), (3, 5)], [(8, 7), (7, 6), (6, 5), (5, 2), (2, 1),
(1, 2), (2, 3), (3, 9), (9, 8)], [(8, 9), (9, 4), (4, 8)], [(7, 4), (4, 6), (6,
7)], [(3, 4), (4, 9), (9, 3)]]
On Wednesday, March 26, 2014 5:34:53 PM UTC-6, Christa Brelsford wrote:
for a simple graph, trace_faces() gives the expected answer for the faces of
a planar graph, as shown below.
import networkx as nx
lat = nx.Graph()
lat.add_edge(1,2)
lat.add_edge(2,3)
lat.add_edge(2,5)
lat.add_edge(3,4)
lat.add_edge(3,5)
lat.add_edge(4,5)
nodes_dict = {}
nodes_dict[1]=(0,0)
nodes_dict[2]=(0,1)
nodes_dict[3]=(0,2)
nodes_dict[4]=(0,3)
nodes_dict[5]=(1,2)
S = Graph(lat)
S.show(vertex_size = 600, pos = nodes_dict)
S.is_planar(set_embedding = True)
s_emb = S.get_embedding()
faces = S.trace_faces(s_emb)
print faces:
[[(1, 2), (2, 3), (3, 4), (4, 5), (5, 2), (2, 1)], [(5, 4), (4, 3), (3,
5)], [(2, 5), (5, 3), (3, 2)]]
There are three faces: one between nodes 2,3 and 5, another between nodes
3,4 and 5,and the outside face of all nodes.
but when I extend the graph:
lat = nx.Graph()
lat.add_edge(1,2)
lat.add_edge(2,3)
lat.add_edge(2,5)
lat.add_edge(3,4)
lat.add_edge(3,5)
lat.add_edge(3,9)
lat.add_edge(4,5)
lat.add_edge(4,6)
lat.add_edge(4,7)
lat.add_edge(4,8)
lat.add_edge(4,9)
lat.add_edge(5,6)
lat.add_edge(6,7)
lat.add_edge(7,8)
lat.add_edge(8,9)
nodes_dict = {}
nodes_dict[1]=(0,0)
nodes_dict[2]=(0,1)
nodes_dict[3]=(0,2)
nodes_dict[4]=(0,3)
nodes_dict[5]=(1,2)
nodes_dict[6]=(1,3)
nodes_dict[7]=(0,4)
nodes_dict[8]=(-1,4)
nodes_dict[9]=(-1,3)
S = Graph(lat)
S.show(vertex_size = 600, pos = nodes_dict)
S.is_planar(set_embedding = True)
s_emb = S.get_embedding()
faces = S.trace_faces(s_emb)
print faces
[[(6, 4), (4, 7), (7, 6)], [(3, 2), (2, 5), (5, 3)], [(5, 4), (4, 6),
(6, 5)], [(7, 8), (8, 9), (9, 3), (3, 5), (5, 6), (6, 7)], [(1, 2), (2,
3), (3, 4), (4, 5), (5, 2), (2, 1)], [(4, 9), (9, 8), (8, 4)], [(7, 4),
(4, 8), (8, 7)], [(3, 9), (9, 4), (4, 3)]]
the face that should exist between just nodes 3,4 and 5 is not found, it's
replaced with a face around nodes 1,2,3,4,5. Any ideas what is wrong, or
other ways of getting an accurate list of the faces in a planar graph?
I'm using 'Sage Version 5.13, Release Date: 2013-12-15'
I realize that trace_faces has been deprecated to just faces() per this
discussion: http://trac.sagemath.org/ticket/15551
but when I run
S.faces()
I get the error
AttributeError: 'Graph' object has no attribute 'faces'
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[sage-support] Re: graph.trace_faces() gives me inconsistent results
On Wednesday, March 26, 2014 5:34:53 PM UTC-6, Christa Brelsford wrote:
for a simple graph, trace_faces() gives the expected answer for the faces of
a planar graph, as shown below.
import networkx as nx
lat = nx.Graph()
lat.add_edge(1,2)
lat.add_edge(2,3)
lat.add_edge(2,5)
lat.add_edge(3,4)
lat.add_edge(3,5)
lat.add_edge(4,5)
nodes_dict = {}
nodes_dict[1]=(0,0)
nodes_dict[2]=(0,1)
nodes_dict[3]=(0,2)
nodes_dict[4]=(0,3)
nodes_dict[5]=(1,2)
S = Graph(lat)
S.show(vertex_size = 600, pos = nodes_dict)
S.is_planar(set_embedding = True)
s_emb = S.get_embedding()
faces = S.trace_faces(s_emb)
print faces:
[[(1, 2), (2, 3), (3, 4), (4, 5), (5, 2), (2, 1)], [(5, 4), (4, 3), (3,
5)], [(2, 5), (5, 3), (3, 2)]]
There are three faces: one between nodes 2,3 and 5, another between nodes
3,4 and 5,and the outside face of all nodes.
but when I extend the graph:
lat = nx.Graph()
lat.add_edge(1,2)
lat.add_edge(2,3)
lat.add_edge(2,5)
lat.add_edge(3,4)
lat.add_edge(3,5)
lat.add_edge(3,9)
lat.add_edge(4,5)
lat.add_edge(4,6)
lat.add_edge(4,7)
lat.add_edge(4,8)
lat.add_edge(4,9)
lat.add_edge(5,6)
lat.add_edge(6,7)
lat.add_edge(7,8)
lat.add_edge(8,9)
nodes_dict = {}
nodes_dict[1]=(0,0)
nodes_dict[2]=(0,1)
nodes_dict[3]=(0,2)
nodes_dict[4]=(0,3)
nodes_dict[5]=(1,2)
nodes_dict[6]=(1,3)
nodes_dict[7]=(0,4)
nodes_dict[8]=(-1,4)
nodes_dict[9]=(-1,3)
S = Graph(lat)
S.show(vertex_size = 600, pos = nodes_dict)
S.is_planar(set_embedding = True)
s_emb = S.get_embedding()
faces = S.trace_faces(s_emb)
print faces
[[(6, 4), (4, 7), (7, 6)], [(3, 2), (2, 5), (5, 3)], [(5, 4), (4, 6),
(6, 5)], [(7, 8), (8, 9), (9, 3), (3, 5), (5, 6), (6, 7)], [(1, 2), (2,
3), (3, 4), (4, 5), (5, 2), (2, 1)], [(4, 9), (9, 8), (8, 4)], [(7, 4),
(4, 8), (8, 7)], [(3, 9), (9, 4), (4, 3)]]
the face that should exist between just nodes 3,4 and 5 is not found, it's
replaced with a face around nodes 1,2,3,4,5. Any ideas what is wrong, or
other ways of getting an accurate list of the faces in a planar graph?
I'm using 'Sage Version 5.13, Release Date: 2013-12-15'
I realize that trace_faces has been deprecated to just faces() per this
discussion: http://trac.sagemath.org/ticket/15551
but when I run
S.faces()
I get the error
AttributeError: 'Graph' object has no attribute 'faces'
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[sage-support] Re: graph.trace_faces() gives me inconsistent results
On Wednesday, March 26, 2014 5:34:53 PM UTC-6, Christa Brelsford wrote:
for a simple graph, trace_faces() gives the expected answer for the faces
of a planar graph, as shown below.
import networkx as nx
lat = nx.Graph()
lat.add_edge(1,2)
lat.add_edge(2,3)
lat.add_edge(2,5)
lat.add_edge(3,4)
lat.add_edge(3,5)
lat.add_edge(4,5)
nodes_dict = {}
nodes_dict[1]=(0,0)
nodes_dict[2]=(0,1)
nodes_dict[3]=(0,2)
nodes_dict[4]=(0,3)
nodes_dict[5]=(1,2)
S = Graph(lat)
S.show(vertex_size = 600, pos = nodes_dict)
S.is_planar(set_embedding = True)
s_emb = S.get_embedding()
faces = S.trace_faces(s_emb)
print faces:
[[(1, 2), (2, 3), (3, 4), (4, 5), (5, 2), (2, 1)], [(5, 4), (4, 3), (3,
5)], [(2, 5), (5, 3), (3, 2)]]
There are three faces: one between nodes 2,3 and 5, another between nodes
3,4 and 5,and the outside face of all nodes.
but when I extend the graph:
lat = nx.Graph()
lat.add_edge(1,2)
lat.add_edge(2,3)
lat.add_edge(2,5)
lat.add_edge(3,4)
lat.add_edge(3,5)
lat.add_edge(3,9)
lat.add_edge(4,5)
lat.add_edge(4,6)
lat.add_edge(4,7)
lat.add_edge(4,8)
lat.add_edge(4,9)
lat.add_edge(5,6)
lat.add_edge(6,7)
lat.add_edge(7,8)
lat.add_edge(8,9)
nodes_dict = {}
nodes_dict[1]=(0,0)
nodes_dict[2]=(0,1)
nodes_dict[3]=(0,2)
nodes_dict[4]=(0,3)
nodes_dict[5]=(1,2)
nodes_dict[6]=(1,3)
nodes_dict[7]=(0,4)
nodes_dict[8]=(-1,4)
nodes_dict[9]=(-1,3)
S = Graph(lat)
S.show(vertex_size = 600, pos = nodes_dict)
S.is_planar(set_embedding = True)
s_emb = S.get_embedding()
faces = S.trace_faces(s_emb)
print faces
[[(6, 4), (4, 7), (7, 6)], [(3, 2), (2, 5), (5, 3)], [(5, 4), (4, 6),
(6, 5)], [(7, 8), (8, 9), (9, 3), (3, 5), (5, 6), (6, 7)], [(1, 2), (2,
3), (3, 4), (4, 5), (5, 2), (2, 1)], [(4, 9), (9, 8), (8, 4)], [(7, 4),
(4, 8), (8, 7)], [(3, 9), (9, 4), (4, 3)]]
the face that should exist between just nodes 3,4 and 5 is not found,
it's replaced with a face around nodes 1,2,3,4,5. Any ideas what is
wrong, or other ways of getting an accurate list of the faces in a planar
graph?
I'm using 'Sage Version 5.13, Release Date: 2013-12-15'
I realize that trace_faces has been deprecated to just faces() per this
discussion: http://trac.sagemath.org/ticket/15551
but when I run
S.faces()
I get the error
AttributeError: 'Graph' object has no attribute 'faces'
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[sage-support] Re: graph.trace_faces() gives me inconsistent results
The problem is not in the trace_faces() method, but in the is_planar()
calculation. The embedding of the second graph is not correct:
S = Graph(lat)
S.show(vertex_size = 600, pos = nodes_dict)
S.is_planar(set_embedding = True)
s_emb = S.get_embedding()
print s_emb
{1: [2], 2: [1, 3, 5], 3: [4, 9, 5, 2], 4: [5, 6, 7, 8, 9, 3], 5: [2, 3,
6, 4], 6: [7, 4, 5], 7: [8, 4, 6], 8: [9, 4, 7], 9: [3, 4, 8]}
This should be a clockwise listing of the neighbors of each node, i.e. node 1
has one neighbor, 2, node 2 has 3 neighbors that are (clockwise) 1,3,5. Node
3, however, has the correct nodes but are not in a clockwise ordering.
On Wednesday, March 26, 2014 5:34:53 PM UTC-6, Christa Brelsford wrote:
for a simple graph, trace_faces() gives the expected answer for the faces of
a planar graph, as shown below.
import networkx as nx
lat = nx.Graph()
lat.add_edge(1,2)
lat.add_edge(2,3)
lat.add_edge(2,5)
lat.add_edge(3,4)
lat.add_edge(3,5)
lat.add_edge(4,5)
nodes_dict = {}
nodes_dict[1]=(0,0)
nodes_dict[2]=(0,1)
nodes_dict[3]=(0,2)
nodes_dict[4]=(0,3)
nodes_dict[5]=(1,2)
S = Graph(lat)
S.show(vertex_size = 600, pos = nodes_dict)
S.is_planar(set_embedding = True)
s_emb = S.get_embedding()
faces = S.trace_faces(s_emb)
print faces:
[[(1, 2), (2, 3), (3, 4), (4, 5), (5, 2), (2, 1)], [(5, 4), (4, 3), (3,
5)], [(2, 5), (5, 3), (3, 2)]]
There are three faces: one between nodes 2,3 and 5, another between nodes
3,4 and 5,and the outside face of all nodes.
but when I extend the graph:
lat = nx.Graph()
lat.add_edge(1,2)
lat.add_edge(2,3)
lat.add_edge(2,5)
lat.add_edge(3,4)
lat.add_edge(3,5)
lat.add_edge(3,9)
lat.add_edge(4,5)
lat.add_edge(4,6)
lat.add_edge(4,7)
lat.add_edge(4,8)
lat.add_edge(4,9)
lat.add_edge(5,6)
lat.add_edge(6,7)
lat.add_edge(7,8)
lat.add_edge(8,9)
nodes_dict = {}
nodes_dict[1]=(0,0)
nodes_dict[2]=(0,1)
nodes_dict[3]=(0,2)
nodes_dict[4]=(0,3)
nodes_dict[5]=(1,2)
nodes_dict[6]=(1,3)
nodes_dict[7]=(0,4)
nodes_dict[8]=(-1,4)
nodes_dict[9]=(-1,3)
S = Graph(lat)
S.show(vertex_size = 600, pos = nodes_dict)
S.is_planar(set_embedding = True)
s_emb = S.get_embedding()
faces = S.trace_faces(s_emb)
print faces
[[(6, 4), (4, 7), (7, 6)], [(3, 2), (2, 5), (5, 3)], [(5, 4), (4, 6),
(6, 5)], [(7, 8), (8, 9), (9, 3), (3, 5), (5, 6), (6, 7)], [(1, 2), (2,
3), (3, 4), (4, 5), (5, 2), (2, 1)], [(4, 9), (9, 8), (8, 4)], [(7, 4),
(4, 8), (8, 7)], [(3, 9), (9, 4), (4, 3)]]
the face that should exist between just nodes 3,4 and 5 is not found, it's
replaced with a face around nodes 1,2,3,4,5. Any ideas what is wrong, or
other ways of getting an accurate list of the faces in a planar graph?
I'm using 'Sage Version 5.13, Release Date: 2013-12-15'
I realize that trace_faces has been deprecated to just faces() per this
discussion: http://trac.sagemath.org/ticket/15551
but when I run
S.faces()
I get the error
AttributeError: 'Graph' object has no attribute 'faces'
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