I’ve previously mentioned graphviz for plotting graphs. In truth, these resemble flowcharts. To create something that looks like a more traditional vertex and edge representation, you might consider NetworkX.

Whereas graphviz is a fairly general purpose utility that is not specific to Python and is developed around the well-defined DOT-format, NetworkX is Python specific but creates very nice graphics. It’s also significantly easier to get something that’s acceptable while probably minimizing the amount of time that you have to monkey with it. With that said, there are multiple layout algorithms that you can invoke to calculate the positions of the elements in the output image, and the only apparent way to get a consistent, well-organized/balanced representation seems to arrange them using the circular layout.

Digraph example:

import networkx as nx
import matplotlib.pyplot as plt

def _main():
    g = nx.DiGraph()

    g.add_edge(2, 3, weight=1)
    g.add_edge(3, 4, weight=5)
    g.add_edge(5, 1, weight=10)
    g.add_edge(1, 3, weight=15)

    g.add_edge(2, 7, weight=1)
    g.add_edge(13, 6, weight=5)
    g.add_edge(12, 5, weight=10)
    g.add_edge(11, 4, weight=15)

    g.add_edge(9, 2, weight=1)
    g.add_edge(10, 13, weight=5)
    g.add_edge(7, 5, weight=10)
    g.add_edge(9, 4, weight=15)

    g.add_edge(10, 3, weight=1)
    g.add_edge(11, 2, weight=5)
    g.add_edge(9, 6, weight=10)
    g.add_edge(10, 5, weight=15)

    pos = nx.circular_layout(g)

    edge_labels = { (u,v): d['weight'] for u,v,d in g.edges(data=True) }

    nx.draw_networkx_nodes(g,pos,node_size=700)
    nx.draw_networkx_edges(g,pos)
    nx.draw_networkx_labels(g,pos)
    nx.draw_networkx_edge_labels(g,pos,edge_labels=edge_labels)

    plt.title("Graph Title")
    plt.axis('off')

    plt.savefig('output.png')
    plt.show()

if __name__ == '__main__':
    _main()

Notice that NetworkX depends on matplotlib to do the actual drawing. The boots (highlighted parts on the edges) represent directedness.

Output:

As I said before, it’s easier to get a nicer representation, but it appears that this is at the cost of flexibility. Notice that in the image, there’s a a tendency to overlap. In fact, all of the edge-labels are dead-center. Since the nodes are arranged in a circle, all edges that cross from one side to another will have labels that overlap in the middle. Technically you can adjust whether the label is left, middle, or right, but it’s limited to that (rather than being calculated on the fly).