2.4: Generating graphs

Last updated
Save as PDF

Page ID: 46579

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

Figure \(\PageIndex{1}\): A complete graph with 10 nodes.

I’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, you can read about them at http://thinkcomplex.com/gen.

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 \(\PageIndex{1}\) 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.