4.5. Generating Graphs

Figure 4.3: A complete graph with 10 nodes.

We’ll start by generating a complete graph, which is a graph where every node is connected to every other.

Here’s a generator function that takes a list of nodes and enumerates all distinct pairs. If you are not familiar with generator functions.

def all_pairs(nodes):
for i, u in enumerate(nodes):
    for j, v in enumerate(nodes):
        if i>j:
            yield u, v

We can use all_pairs to construct a complete graph:

def make_complete_graph(n):
    G = nx.Graph()
    nodes = range(n)
    G.add_nodes_from(nodes)
    G.add_edges_from(all_pairs(nodes))
    return G

make_complete_graph takes the number of nodes, n, and returns a new Graph with n nodes and edges between all pairs of nodes.

The following code makes a complete graph with 10 nodes and draws it:

complete = make_complete_graph(10)
nx.draw_circular(complete,
             node_color=COLORS[2],
             node_size=1000,
             with_labels=True)

Figure 4.3 shows the result. Soon we will modify this code to generate ER graphs, but first we’ll develop functions to check whether a graph is connected.

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