Partitions of Graphs II: Graphs

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:

graph1graph2graph3graph4graph5graph6fisheyeviewLoads 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

graph1

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

Advertisements
This entry was posted in graphs. Bookmark the permalink.

2 Responses to Partitions of Graphs II: Graphs

  1. Pingback: Partitions of Graphs III: Ramanujan meets Kevin Bacon « MATH with my KIDS

  2. Pingback: Partitions of Graphs IV: Partitions of Graphs « MATH with my KIDS

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s