This is the second in a series. The first being Partitions of Graphs I.

A graph is what most people call a network. It’s a bunch of dots (called nodes) connected by lines (called edges). Here are some pictures of graphs:

Loads of real-world systems can be modeled by graphs. Some examples are: the Web, with pages as nodes, and hyperlinks as edges (Google makes lots of money off of having a good mathematical grasp of the graph-theory intrinsic to the Web); Maps, with cities as nodes and freeways as edges; A chess game, with position as nodes, and legal moves from one position to the next as edges.

Mostly I like graphs because they are fun to draw and play with.

For this series I’m going to have to draw some graphs. I think what I want to do here is go totally old school and draw my graphs as ascii art. I do this because it is easy and it should be sufficient for my purposes. Most graphs you wouldn’t be able to draw very well with ascii art, but the ones I will need I don’t think I will have any problems with.

So I will use

o

as my nodes and these lines

- \ / |

as my edges. The graph below

becomes:

o
/
o o
|/ \
o o
| |
o o

Ok, not as pretty, and I haven’t labeled the nodes here, but humor me. Next post I’ll talk a little more about graphs and partitions of whole numbers and why I want to relate the two. Mean while, have fun drawing some graphs.

Part III: Ramanujan Meets Kevin Bacon

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