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 GraphViz^{1}.

**RandomSubset(p)**

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:

**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:**

**A focus on the heavily linked part of for x = 10 000, y = 5**

**Here’s one for 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; }