## Barabasi-Erdos Graph¶

A Barabasi-Albert graph is a random graph https://en.wikipedia.org/wiki/Barab%C3%A1si%E2%80%93Albert_model.

In [3]:
import plotly.plotly as py
from plotly.graph_objs import *
import plotly.tools as tls
import networkx as nx

In [4]:
nr_nodes=150
G=nx.barabasi_albert_graph(nr_nodes, 5)

In [5]:
pos=nx.random_layout(G, dim= 2)# get  node positions

In [6]:
clusteringC=[nx.clustering(G,v) for v in G.nodes()]#list of clustering coefficients
degree=[G.degree(v) for v in G.nodes()] # list of node degrees
labels=['Node deg: '+ str(G.degree(v))+'<br>Clust coeff: '\
+'{:.5f}'.format(nx.clustering(G,v))  for v in G.nodes()]#labels for nodes


Define the lists of node coordinates, Xn, Yn, and the lists of coordinates Xe, Ye, for ends of edges:

In [35]:
L=len(pos)
X=[]
Y=[]
Xn=[pos[k][0] for k in range(L)]
Yn=[pos[k][1] for k in range(L)]
Xe=[]
Ye=[]
for edge in G.edges():
Xe+=[pos[edge[0]][0],pos[edge[1]][0], None]
Ye+=[pos[edge[0]][1],pos[edge[1]][1], None]


We define two Plotly plots for the same Barabasi-Albert graph. In the first one the node colors are assigned according to their clustering coefficients and in the second one, according to the node degree.

Custom colorscale to plot the nodes in one of the two subplots:

In [12]:
nyrev_cs=[[0.0, '#FFFFE0'],
[0.06666666666666667, '#FFEEC1'],
[0.13333333333333333, '#FFDEA7'],
[0.2, '#FFCB91'],
[0.26666666666666666, '#FFB880'],
[0.3333333333333333, '#FFA474'],
[0.4, '#FE906A'],
[0.4666666666666667, '#F87D64'],
[0.5333333333333333, '#F06A5E'],
[0.6, '#E75758'],
[0.6666666666666666, '#DB4551'],
[0.7333333333333333, '#CF3447'],
[0.8, '#C0223B'],
[0.8666666666666667, '#B0122C'],
[0.9333333333333333, '#9E051B'],
[1.0, '#8B0000']]


Define Plotly Scatter objects for edges (trace 1) and nodes (trace2 and trace3):

In [67]:
trace1=Scatter(x=Xe,
y=Ye,
mode='lines',
line=Line(color='rgb(210,210,210)', width=0.5),
hoverinfo='none'
)
trace2=Scatter(x=Xn,
y=Yn,
mode='markers',
name='B-A',
marker=Marker(symbol='dot',
size=10,
color=clusteringC,
colorscale=nyrev_cs, #custom colorscale
#colorbar={'title':'Clustering coeff', 'titleside':'top'},
line=Line(color='rgb(50,50,50)', width=0.5)
),
text=labels,
hoverinfo='text'
)
trace3=Scatter(x=Xn,
y=Yn,
mode='markers',
name='B-A',
marker=Marker(symbol='dot',
size=10,
color=degree,
colorscale='YIGnBu', #Plotly colorscale
reversescale=True,
#colorbar={'title':'Node degree', 'titleside':'top'},
line=Line(color='rgb(50,50,50)', width=0.5)
),
text=labels,
hoverinfo='text'
)


Subplot titles:

In [68]:
titles=('Colors assigned according to the<br>node clustering coefficient',
'Colors assigned according to the<br>node degree')

In [75]:
figure = tls.make_subplots(rows=1, cols=2, subplot_titles=titles,
horizontal_spacing=0.025,
print_grid=True)

This is the format of your plot grid:
[ (1,1) x1,y1 ]  [ (1,2) x2,y2 ]


In [76]:
axis=dict(showline=False, # hide axis line, grid, ticklabels and  title
zeroline=False,
showgrid=False,
showticklabels=False,
title=''
)
def make_XAxis():
xaxis = XAxis()
xaxis.update(axis)
return xaxis
def make_YAxis():
yaxis = YAxis()
yaxis.update(axis)
return yaxis

In [77]:
width=1000
height=500

figure['layout'].update(title= 'Barabasi-Albert Graph of parameters (m,n)=(150, 5)',
font= Font(size=14),
showlegend=False,
autosize=False,
width=width,
height=height,
margin=Margin(
l=40,
r=40,
b=85,
t=120,
),
hovermode='closest',
)

In [78]:
figure.append_trace(trace1, 1, 1)
figure.append_trace(trace2, 1, 1)
figure.append_trace(trace1, 1, 2)
figure.append_trace(trace3, 1, 2)

In [79]:
for s in [1,2]:
figure['layout'].update({'xaxis{}'.format(s): make_XAxis()})# set xaxis style
figure['layout'].update({'yaxis{}'.format(s): make_YAxis()})# set yaxis style

In [80]:
py.sign_in('empet', '')
py.iplot(figure, filename='Barabasi-Albert-Graph')

Out[80]:
u'https://plot.ly/~empet/8024'

Click on the image below to access the interactive plots:

In [2]:
from IPython.core.display import HTML
def  css_styling():