I have a few idaes for startups with a graph-like structure and found myself exploring the topic of graph visualization. I decided to see if I could generate some graphs containing hundreds of thousands of edges. Tools of choice: bash, python, and GraphViz1.


Using my template I first made a graph of a random subset of (p * 100)% of the 2-tuples in the cartesian product between the first X integers:

[(a, b) for a in range(_X_) for b in range(_X_) if random() < p]

Here’s the middle of the graph for p=0.02:

Graph of random subset (2%) of the possible pairings of the first 10,000 numbers.

CommonFactors(x, y)

Next, I decided to see what the graph of integers < X that have more than Y factors in common.

[(a, b) for a in range(X) for b in range(X) if len(common_factors(a,b)) > Y]


Here’s the graph for x=10 000, y=5:

This is a graph visualization with X=10 000 and Y=5 A focus on the heavily linked part of for x = 10 000, y = 5

A GraphViz example of integers with common factors – point shape used for nodes

Here’s one for x=10 000, y=30

x=10 000 y=30

I found them all to be quite beautiful.

The Code

If you want to check out the source code, here’s the github: https://github.com/stephenbalaban/biggraphs.

Note: The first image is a section of an earlier iteration of the CommonFactors graph.

[1] GraphViz project: http://graphviz.org - I used the point shape for the nodes here’s the part of the code that describes my graph style:

graph gengraph {
        graph [bgcolor="#FFFFFF", outputorder="edgesfirst", dpi=1000];
        node [width=0.0008, fixedsize=true, shape=point, color="#00000099"];
        edge [penwidth=0.1, color="#00000099"]graph [bgcolor="#FFFFFF", outputorder="edgesfirst", dpi=1000];
        a -- b;
        b -- a;
        a -- c;
        c -- a;
        a -- d;
        b -- d;
        c -- d;

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