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shoke/colorgraph.py

Created May 16, 2011 07:20
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Graphene
Raw
colorgraph.py
import networkx as nx
import matplotlib as mat
import matplotlib.pyplot as plt
import numpy as np
# Colors each node in the given graph based on the data
# Set provided
def color_graph(graph, d, cmap):
col_graph = nx.Graph()
#normalize the data and create an array of colors that will
#correspond to the nodes in the graph
data = (normalize(d))
color_array = []
for j in range(len(data)):
color = cmap(data[j])
color_array.append( color )
i = 0
# add the color to each node
for node in graph.nodes():
red = int(255*color_array[i][0])
blu = int(255*color_array[i][1])
gre = int(255*color_array[i][2])
alp = color_array[i][3]
i = i + 1
col_graph.add_node(node,{'viz':{'color':dict(r=red,b=blu,g=gre,a=alp)}})
col_graph.add_edges_from(graph.edges())
return col_graph
# Normalizes the given data between 0 and 1
def normalize(data):
d = []
min = float(np.min(data))
max = float(np.max(data))
data_range = max - min
for j in range(len(data)):
d.append( ( float(data[j]) - min) / data_range )
return d
# Utilizes the networkx draw_networkx function
# Useful for small graphs
def graphene_graph(g, data, cmap = plt.cm.Blues):
min = float(np.min(data))
max = float(np.max(data))
nx.draw_networkx(g, cmap = cmap, vmin = min, vmax = max, node_color = data)
plt.show()
Raw
graphene.py
import networkx as nx
import matplotlib as mat
import matplotlib.pyplot as plt
import colorgraph
# Builds a graphene sheet with the given number of rows and columns.
# If wrap is set to true it will roll it up
def build_graph(rows, columns, wrap):
g = nx.Graph()
# creates the first complete hexagon
for i in range(6):
if (i+1) > 1:
g.add_edge(i+1,i)
g.add_edge(6,1)
# top of the first hexagon, start and end of the next hexagon
start = 4
end = 5
numNodes = 6
# if the number of hexagons in the row is greater than 1
if rows > 1:
for j in range(rows-1):
s = start
# 2 nodes already placed, adds the next 4
for addnodes in range(4):
g.add_edge(s, numNodes+1)
numNodes += 1
s = numNodes
g.add_edge(numNodes, end)
start += 4
end += 4
evenColumn = True
secondColumn = True
connection = 1
# startingNode is the node the NEXT column will start at
# (aka the bottom of the one being drawn)
startingNode = numNodes + 1
# start is your current postion
start = startingNode
# if there is more than one column
if columns > 1:
for k in range(columns-1):
# even vs. odd columns start and end differently
if evenColumn:
# the connection to the last finished column
# the first hexagon in each new column has one extra node
connection += 2
if not(k == (columns-2)):
g.add_edge(start, start+1)
start += 1
numNodes +=1
g.add_edge(start, start+1)
g.add_edge(start, connection)
numNodes += 1
for l in range(rows -1):
# the second column is a special case
if secondColumn:
connection += 4
else:
connection += 2
start += 1
g.add_edge(start-1, start)
g.add_edge(start, start+1)
start += 1
g.add_edge(start, connection)
numNodes += 2
# finish column
if not(k == (columns-2)):
g.add_edge(numNodes , numNodes +1)
numNodes +=1
evenColumn = False
secondColumn = False
connection = startingNode
startingNode = numNodes
start = numNodes +1
else:
g.add_edge(start, connection)
g.add_edge(start, start+1)
start += 1
g.add_edge(start, start+1)
start += 1
connection += 2
g.add_edge(start, connection)
numNodes += 3
for l in range(rows -1):
connection += 2
g.add_edge(start+1, start)
start += 1
g.add_edge(start, start+1)
start += 1
g.add_edge(start, connection)
numNodes += 2
# finish column
start += 1
evenColumn = True
connection = startingNode
startingNode = start
# are we rolling the sheet?
if wrap and (rows > 0):
g.remove_node( 2 + (rows * 4) - 1 )
g.add_edge( 2 + (rows * 4) , 1 )
g.remove_node( 2 + (rows * 4) - 2 )
g.add_edge( 2 + (rows * 4) - 3, 2 )
start = 3 + (rows * 4)
for k in range(columns-1):
end = 2 * rows + start
g.remove_node( end )
g.add_edge( end - 1, start )
start = end + 1
return g
def build_and_color(rows,columns,wrap,data,cmap = plt.cm.Blues, filename = "test.gexf"):
g = build_graph(rows,columns,wrap)
g = colorgraph.color_graph(g,data,cmap)
nx.write_gexf(g,filename)
# Builds a graphene sheet with the given number of rows and columns.
# The sheet has a defected column running through the optionally passed
# arg. Otherwise it defaults to the center.
def defected_graphene_graph(rows, columns, defect = 0):
g = nx.Graph()
index = 0;
if( columns <= 2 ):
print "Must have more than two columns."
return g
if( rows < 2 ):
print "Must have more than 1 row."
return g
if defect[index] == 1:
print "Defect wire cannot be on edge column."
if defect[index] == columns:
print "Defect wire cannot be on edge column."
if (defect[index] == 0) :
defect[index] = int(columns/2) + 1
# creates the first complete hexagon
for i in range(6):
if (i+1) > 1:
g.add_edge(i+1,i)
g.add_edge(6,1)
# top of the first hexagon, start and end of the next hexagon
start = 4
end = 5
numNodes = 6
# if the number of hexagons in the row is greater than 1
if rows > 1:
for j in range(rows-1):
s = start
# 2 nodes already placed, adds the next 4
for addnodes in range(4):
g.add_edge(s, numNodes+1)
s = numNodes + 1
numNodes += 1
g.add_edge(numNodes, end)
start += 4
end += 4
evenColumn = True
secondColumn = True
connection = 1
# startingNode is the node the NEXT column will start at
# (aka the bottom of the one being drawn)
startingNode = numNodes + 1
# start is your current postion
start = startingNode
afterDefect = False
after2 = False
# if there is more than one column
if columns > 1:
for k in range(columns-1):
if( k+2 == defect[index] ):
if evenColumn:
connection += 2
g.add_edge(connection, start)
g.add_edge(start, start+1)
g.add_edge(start+1, start+2)
g.add_edge(start+1, start+2)
g.add_edge(start+2, start+3)
g.add_edge(start+3, start+4)
numNodes += 5
# the second column is a special case
if secondColumn:
connection += 4
else:
connection += 2
g.add_edge(connection, start+4)
start += 4
evenRow = True
for l in range(rows -2):
if evenRow:
# the second column is a special case
if secondColumn:
connection += 4
elif afterDefect:
connection += 4
else:
connection += 2
g.add_edge(start, start+1)
g.add_edge(start+1, connection)
start = start -1
g.add_edge(start, start+3)
g.add_edge(start+3, start + 4)
g.add_edge(start+2, start + 4)
start += 4
numNodes += 3
evenRow = False
else:
# the second column is a special case
if secondColumn:
connection += 4
else:
connection += 2
g.add_edge(start, start+1)
g.add_edge(start+2, start+1)
g.add_edge(start+2, start+3)
g.add_edge(connection, start+3)
numNodes += 3
start += 3
evenRow = True
if not evenColumn:
if evenRow:
# the second column is a special case
if secondColumn:
connection += 4
else:
connection += 2
g.add_edge(start, start+1)
if not afterDefect:
g.add_edge(start+1, connection)
start = start -1
g.add_edge(start, start+3)
g.add_edge(start+3, start + 4)
g.add_edge(start+2, start + 4)
start += 2
if afterDefect:
g.add_edge(start, start+3)
g.add_edge(start+3, start+4)
g.add_edge(start+4, connection-2)
start += 2
numNodes += 5
evenRow = False
else:
connection += 2
g.add_edge(start, start+1)
start += 1
g.add_edge(start, start+1)
start += 1
g.add_edge(start, start+1)
start += 1
g.add_edge(start, connection)
numNodes += 3
connection = startingNode + 1
start = numNodes +1
evenColumn = not evenColumn
startingNode = numNodes
secondColumn = False
afterDefect = True
if not(index == (len(defect)-1)):
index = index + 1
# even vs. odd columns start and end differently
elif evenColumn:
# the connection to the last finished column
# the first hexagon in each new column has one extra node
connection += 2
if not(k == (columns-2)):
g.add_edge(start, start+1)
start += 1
numNodes +=1
g.add_edge(start, start+1)
if afterDefect:
#connection += 1
evenRow = True
g.add_edge(start, connection)
numNodes += 1
for l in range(rows -1):
# the second column is a special case
if secondColumn:
connection += 4
elif afterDefect:
if evenRow:
connection += 4
evenRow = False
else:
connection += 2
evenRow = True
else:
connection += 2
start += 1
g.add_edge(start-1, start)
g.add_edge(start, start+1)
start += 1
g.add_edge(start, connection)
numNodes += 2
# finish column
if not(k == (columns-2)):
g.add_edge(numNodes , numNodes +1)
numNodes +=1
evenColumn = False
secondColumn = False
connection = startingNode
if afterDefect:
connection += 1
elif after2:
g.add_edge(numNodes, numNodes + 1)
numNodes += 1
startingNode = numNodes
start = numNodes +1
afterDefect = False
else:
g.add_edge(start, connection)
g.add_edge(start, start+1)
start += 1
g.add_edge(start, start+1)
start += 1
if afterDefect:
g.add_edge(start, start+1)
start += 1
connection += 1
evenRow = True
else:
connection += 2
g.add_edge(start, connection)
numNodes += 3
for l in range(rows -1):
if afterDefect:
if evenRow:
connection += 4
evenRow = False
else:
connection += 2
evenRow = True
else:
connection += 2
g.add_edge(start+1, start)
start += 1
g.add_edge(start, start+1)
start += 1
if( l == (rows-2) ):
if afterDefect:
g.add_edge(start +1, start)
if evenRow:
g.add_edge(start +1, connection-1)
else:
g.add_edge(start +1, connection-3)
numNodes += 3
else:
g.add_edge(start, connection)
numNodes += 2
else:
g.add_edge(start, connection)
numNodes += 2
# finish column
start += 1
evenColumn = True
if after2:
after2 = False
if afterDefect:
startingNode += 1
after2 = True
start += 1
connection = startingNode
startingNode = start
afterDefect = False
return g
Raw
miscgraph.py
import networkx as nx
import random
# Adds the number of defects specified to the graph. Removes the nodes randomly
# and all adjacent edges
def add_defects(graph, number):
# do we have enough nodes?
if (number >= len(graph.nodes()) ):
print "The number of defects must be less than the size of the graph"
return graph
# randomly generate nodes to pull
defects = random.sample(graph.nodes(), number)
for i in range(len(defects)):
graph.remove_node(defects[i])
return graph
def stonewales_defect(graph, node):
neighbors = graph.neighbors(node)
new_graph = graph
node2 = 0
if neighbors[0] < node:
if neighbors[1] < node:
node2 = node-1
elif neighbors[2] < node:
node2 = node-1
else:
node2 = node
node = node+1
elif neighbors[0] > node:
if neighbors[1] > node:
node2 = node
node = node+1
elif neighbors[2] > node:
node2 = node
node = node+1
else:
node2 = node-1
if(len(graph.neighbors(node)) < 3):
print "Bad node"
return graph
if(len(graph.neighbors(node2)) < 3):
print "Bad node"
return graph
new_graph.remove_edge(node, node+1)
new_graph.remove_edge(node, node-1)
new_graph.add_edge(node,node-2)
new_graph.remove_edge(node2, node2-1)
new_graph.add_edge(node2,node2+2)
new_graph.add_edge(node,node2)
return new_graph
# Builds a complete two-node graph
def build_two_node():
return nx.complete_graph(2)
# Builds a complete three-node graph
def build_three_node():
return nx.complete_graph(3)
# Builds a complete four-node graph
def build_four_node():
return nx.complete_graph(4)
Raw
quantumgraph.py
import networkx as nx
def get_hamiltonian(g):
return -0.5 * nx.laplacian(g)
@ellisonbg
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OK, great start. As a next step, let's put the main part of the code in a python function that takes the input parameters (rows, columns) and returns a networkx graph object. After that, I think we want to begin to work on characterizing the sheet using the lattice unit vectors a_1 and a_2. These provide a very powerful and exact way of describing any sheet of graphene (or nanotube). A good starting point for learning about this is the Wikipedia page on Carbon Nanotubes: http://en.wikipedia.org/wiki/Carbon_nanotube

I will have research office hours this Wed and we can talk more about this then.

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