def refineColors(G: graph):
a = dict()
aPrev = dict()
neighbours = generateNeighbourList(G)
# define a number that gives a color that has not yet been chosen
nextColor = 0
# Fill a with colors related to the degree of the vertex
for v in G.V():
a[v] = len(neighbours[v])
nextColor = max(a[v] + 1, nextColor)
# while the colors still change after an iteration
while aPrev != a:
aPrev = a
a = dict()
nbColors = getNeighbourColors(neighbours, aPrev)
# for each vertex u in G.V()
for i in range(len(G.V())):
u = G.V()[i]
# initialize nc, the new color of u
nc = a.get(u, aPrev[u])
# create a set "same" that will contain all vertices v that are "equal" to the current vertex u
same = set()
# for every unchecked vertex v
for v in G.V()[i + 1 :]:
# if the vertices were "equal" and not exactly the same
if u != v and aPrev[u] == aPrev[v]:
# Check if they are still "equal"
if not haveSameNeighbours(u, v, nbColors):
# they are not equal anymore, if we haven't updated nc already, do it now
if nc == aPrev[u]:
nc = nextColor
nextColor += 1
else:
# they are still equal, add the vertex to our "same" set
same.add(v)
# update the a[v] of every v in same
for v in same:
# If nc and a[v] (or the previous a[v]) differ, change a[v]
if nc != a.get(v, aPrev[v]):
a[v] = nc
a[u] = nc
# set the colornums
for v in a:
v.colornum = a[v]
return a
def countTreeAutomorphismsRS(G, visualize=False):
p = generatePartitions(G)
n = generateNeighbourList(G)
degrees = dict()
for v in G.V():
degree = len(n[v])
degreeSet = degrees.get(degree, 0)
if degreeSet:
degreeSet.add(v)
else:
degrees[degree] = {v}
colorOf = dict()
for color in p:
for v in color:
colorOf[v] = color
queue = []
done = set()
automorphisms = 1
for c in p:
if len(c) == 1:
queue.append((pickFromSet(c), None))
break
if not queue:
for c in p:
if len(c) == 2:
r, l = c
if True or l in n[r]:
queue.append((r, None))
break
while queue:
vertex, parent = queue[-1]
color = colorOf[vertex]
del queue[-1]
for v in n[vertex] - done:
if v not in done:
queue.append((v, vertex))
done |= colorOf[v]
if parent:
automorphisms *= math.factorial(len(n[parent] & color))**(len(colorOf[parent]))
else:
automorphisms *= math.factorial(len(color))
if visualize:
drawProgress(G, vertex, color, done, queue)
done |= color
if visualize:
drawProgress(G, None, set(), done, queue)
return automorphisms
def generatePartitions(G, usecolors=False):
neighbours = generateNeighbourList(G)
p = []
pSplit = []
degrees = dict()
for v in G.V():
degree = len(neighbours[v])
if degrees.get(degree, -1) == -1:
degrees[degree] = {v}
else:
degrees[degree].add(v)
if usecolors:
p = generatePfromColors(G)
pSplit = generatePfromColors(G)
else:
for k in degrees:
p.append(degrees[k])
pSplit.append(degrees[k])
w = set(range(len(p)))
while w:
#print("w: ", w)
#print("wl: ", [(c, len(p[c])) for c in w])
aN = w.pop()
a = p[aN]
nbs = set()
for va in a:
nbs |= neighbours[va]
# print("nbs: ", nbs)
for color in pSplit:
x = nbs & color
# print("nbs & color: ", x)
if x:
for yN in range(len(p)):
if len(p[yN]) > 1:
y = p[yN]
both = x & y
ynotx = y - x
if both and ynotx:
p[yN] = both
p.append(ynotx)
if yN in w:
w.add(len(p) - 1)
else:
if len(both) <= len(ynotx):
w.add(yN)
else:
w.add(len(p) - 1)
return p
def refineColorsv2(G: graph, useColornums=False):
# a is a dict that contains a vertex as key and a color as value
a = dict()
# the old a, from the previous iteration
aPrev = dict()
# aRev (a reversed) contains a color as key and a set of vertices that have that color as value
aRev = dict()
# the a reversed dict of the previous iteration
aRevPrev = dict()
# generate a dict of vertex -> vertices that contains all the neighbours of the key vertex
neighbours = generateNeighbourList(G)
# define a number that gives a color that has not yet been chosen
nextColor = 0
# Fill a with colors related to the degree of the vertex
for v in G.V():
# color of v = the degree of v (number of neighbours)
if not useColornums:
a[v] = len(neighbours[v])
else:
a[v] = v.colornum
addToRevDict(aRev, a[v], v)
# make sure nextColor is always higher than the highest color that was already used
nextColor = max(a[v] + 1, nextColor)
# while the colors still change after an iteration
while aPrev != a:
# set the Prev dicts to the previous values of a and aRev and reset a and aRev
aPrev = a
aRevPrev = aRev
a = dict()
aRev = dict()
nbColors = getNeighbourColors(neighbours, aPrev)
# pus all the vertices that we have already refined in the set done so we won't have to check them again
done = set()
# for each vertex u in G.V()
for u in G.V():
# if u has already been refined earlier in this iteration, skip it now
if u in done:
continue
# initialize nc, the new color of u
nc = a.get(u, aPrev[u])
# create a set "same" that will contain all vertices v that are "equal" to the current vertex u
same = set()
# for every vertex v that was equal
for v in aRevPrev[aPrev[u]]:
# if the vertices were "equal" and not exactly the same
if u != v:
# Check if they are still "equal"
if not haveSameNeighbours(u, v, nbColors):
# they are not equal anymore, if we haven't updated nc already, do it now
if nc == aPrev[u]:
nc = nextColor
nextColor += 1
else:
# they are still equal, add the vertex to our "same" set
same.add(v)
# update the a[v] of every v in same
for v in same:
# If nc and a[v] (or the previous a[v]) differ, change a[v]
if nc != a.get(v, aPrev[v]):
a[v] = nc
addToRevDict(aRev, nc, v)
done.add(v)
a[u] = nc
addToRevDict(aRev, nc, u)
# set the colornums
for v in a:
v.colornum = a[v]
return a
def countTreeAutomorphismsLS(G, visualize=False):
p = generatePartitions(G)
n = generateNeighbourList(G)
degrees = dict()
for v in G.V():
degree = len(n[v])
degreeSet = degrees.get(degree, 0)
if degreeSet:
degreeSet.add(v)
else:
degrees[degree] = {v}
colorOf = dict()
for color in p:
for v in color:
colorOf[v] = color
queue = []
done = set()
for color in p:
if len(color) > 1 and color <= degrees[1]:
queue.append(color)
done = done | color
automorphisms = 1
while queue: # is not empty
newQueue = []
for color in queue:
v = pickFromSet(color)
if visualize:
drawProgress(G, v, color, done, queue)
parent = None
for neighbour in n[v]:
if len(n[neighbour] & color) > 1 :
parent = neighbour
break
if parent is None:
unvisitedNeighbours = n[v] - done
if len(unvisitedNeighbours) == 1:
parent = unvisitedNeighbours.pop()
elif len(unvisitedNeighbours) > 1:
newQueue.append(color)
continue
if parent:
if len(colorOf[parent]) > 1 and parent not in done:
newQueue.append(colorOf[parent])
automorphisms *= math.factorial(len(n[parent] & color))**(len(colorOf[parent]))
done |= color
else:
if len(color) == 2 and len(color&n[v]) == 1:
automorphisms *= 2
queue = newQueue
for c in queue:
done |= c
if visualize:
drawProgress(G, None, set(), done, queue)
return automorphisms