2.2: NetworkX

Figure \(\PageIndex{1}\): An undirected graph that represents driving time between cities.

To represent graphs, we’ll use a package called NetworkX, which is the most commonly used network library in Python. You can read more about it at http://thinkcomplex.com/netx, but I’ll explain it as we go along.

We can create a directed graph by importing NetworkX (usually imported as nx) and instantiating nx.DiGraph:

import networkx as nx 
G = nx.DiGraph()

At this point, G is a DiGraph object that contains no nodes and no edges. We can add nodes using the add_node method:

G.add_node('Alice') 
G.add_node('Bob') 
G.add_node('Chuck')

Now we can use the nodes method to get a list of nodes:

>>> list(G.nodes()) 
NodeView(('Alice', 'Bob', 'Chuck'))

The nodes method returns a NodeView, which can be used in a for loop or, as in this example, used to make a list.

Adding edges works pretty much the same way:

G.add_edge('Alice', 'Bob') 
G.add_edge('Alice', 'Chuck') 
G.add_edge('Bob', 'Alice') 
G.add_edge('Bob', 'Chuck')

And we can use edges to get the list of edges:

>>> list(G.edges()) 
[('Alice', 'Bob'), ('Alice', 'Chuck'), 
 ('Bob', 'Alice'), ('Bob', 'Chuck')]

NetworkX provides several functions for drawing graphs; draw_circular arranges the nodes in a circle and connects them with edges:

nx.draw_circular(G,
                 node_color=COLORS[0],
                 node_size=2000,
                 with_labels=True)

That’s the code I use to generate Figure 2.1.1. The option with_labels causes the nodes to be labeled; in the next example we’ll see how to label the edges.

To generate Figure \(\PageIndex{1}\), I start with a dictionary that maps from each city name to its approximate longitude and latitude:

positions = dict(Albany=(-74, 43),
                 Boston=(-71, 42),
                 NYC=(-74, 41),
                 Philly=(-75, 40))

Since this is an undirected graph, I instantiate nx.Graph:

G = nx.Graph()

Then I can use add_nodes_from to iterate the keys of positions and add them as nodes:

G.add_nodes_from(positions)

Next I’ll make a dictionary that maps from each edge to the corresponding driving time:

drive_times = {('Albany', 'Boston'): 3, 
               ('Albany', 'NYC'): 4, 
               ('Boston', 'NYC'): 4, 
               ('NYC', 'Philly'): 2}

Now I can use add_edges_from, which iterates the keys of drive_times and adds them as edges:

G.add_edges_from(drive_times)

Instead of draw_circular, which arranges the nodes in a circle, I’ll use draw, which takes the position dictionary as the second parameter:

nx.draw(G, positions, 
        node_color=COLORS[1], 
        node_shape='s', 
        node_size=2500, 
        with_labels=True)

draw uses positions to determine the locations of the nodes.

To add the edge labels, we use draw_networkx_edge_labels:

nx.draw_networkx_edge_labels(G, positions,
                             edge_labels=drive_times)

The edge_labels parameter expects a dictionary that maps from each pair of nodes to a label; in this case, the labels are driving times between cities. And that’s how I generated Figure \(\PageIndex{1}\).

In both of these examples, the nodes are strings, but in general they can be any hashable type.