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

import networkx as nx
import matplotlib.pyplot as plt

G = nx.DiGraph()
    [('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)

Red edges