how to draw directed graphs using networkx in python?

Fully fleshed out example with arrows for only the red edges:

import networkx as nx
import matplotlib.pyplot as plt

G = nx.DiGraph()
G.add_edges_from(
    [('A', 'B'), ('A', 'C'), ('D', 'B'), ('E', 'C'), ('E', 'F'),
     ('B', 'H'), ('B', 'G'), ('B', 'F'), ('C', 'G')])

val_map = {'A': 1.0,
           'D': 0.5714285714285714,
           'H': 0.0}

values = [val_map.get(node, 0.25) for node in G.nodes()]

# Specify the edges you want here
red_edges = [('A', 'C'), ('E', 'C')]
edge_colours = ['black' if not edge in red_edges else 'red'
                for edge in G.edges()]
black_edges = [edge for edge in G.edges() if edge not in red_edges]

# Need to create a layout when doing
# separate calls to draw nodes and edges
pos = nx.spring_layout(G)
nx.draw_networkx_nodes(G, pos, cmap=plt.get_cmap('jet'), 
                       node_color = values, node_size = 500)
nx.draw_networkx_labels(G, pos)
nx.draw_networkx_edges(G, pos, edgelist=red_edges, edge_color='r', arrows=True)
nx.draw_networkx_edges(G, pos, edgelist=black_edges, arrows=False)
plt.show()

Red edges

I only put this in for completeness. I've learned plenty from marius and mdml. Here are the edge weights. Sorry about the arrows. Looks like I'm not the only one saying it can't be helped. I couldn't render this with ipython notebook I had to go straight from python which was the problem with getting my edge weights in sooner.

import networkx as nx
import numpy as np
import matplotlib.pyplot as plt
import pylab

G = nx.DiGraph()

G.add_edges_from([('A', 'B'),('C','D'),('G','D')], weight=1)
G.add_edges_from([('D','A'),('D','E'),('B','D'),('D','E')], weight=2)
G.add_edges_from([('B','C'),('E','F')], weight=3)
G.add_edges_from([('C','F')], weight=4)


val_map = {'A': 1.0,
                   'D': 0.5714285714285714,
                              'H': 0.0}

values = [val_map.get(node, 0.45) for node in G.nodes()]
edge_labels=dict([((u,v,),d['weight'])
                 for u,v,d in G.edges(data=True)])
red_edges = [('C','D'),('D','A')]
edge_colors = ['black' if not edge in red_edges else 'red' for edge in G.edges()]

pos=nx.spring_layout(G)
nx.draw_networkx_edge_labels(G,pos,edge_labels=edge_labels)
nx.draw(G,pos, node_color = values, node_size=1500,edge_color=edge_colors,edge_cmap=plt.cm.Reds)
pylab.show()

enter image description here

Instead of regular nx.draw you may want to use:

nx.draw_networkx(G[, pos, arrows, with_labels])

For example:

nx.draw_networkx(G, arrows=True, **options)

You can add options by initialising that ** variable like this:

options = {
    'node_color': 'blue',
    'node_size': 100,
    'width': 3,
    'arrowstyle': '-|>',
    'arrowsize': 12,
}

Also some functions support the directed=True parameter In this case this state is the default one:

G = nx.DiGraph(directed=True)

The networkx reference is found here.

Graph with arrows image

You need to use a directed graph instead of a graph, i.e.

G = nx.DiGraph()

Then, create a list of the edge colors you want to use and pass those to nx.draw (as shown by @Marius).

Putting this all together, I get the image below. Still not quite the other picture you show (I don't know where your edge weights are coming from), but much closer! If you want more control of how your output graph looks (e.g. get arrowheads that look like arrows), I'd check out NetworkX with Graphviz.

enter image description here