1210431871:::Mike Hardy:::hardy@math.umn.edu::::::The first and second are Venn diagrams.

The third and fourth are graphs. 1210483279:::Wendy:::::::::Oh man, the Nature of God is hilarious. 1210504740:::Paul in Cambridge:::ermanaricus-ainaswirlything-gmailperiodcom:::http://steamboatsnorri.livejournal.com/:::On the first one, I've never seen a more fitting place to comment: SWEET ZOMBIE JESUS! 1210541789:::Diana Hsieh:::diana@dianahsieh.com:::http://www.dianahsieh.com/blog:::Mike says: "The first and second are Venn diagrams. The third and fourth are graphs."

My Oxford American Dictionary defines a diagram as "a simplified drawing showing the appearance, structure, or workings of something; a schematic representation." By that definition, all four thingies are diagrams.

In contrast, a graph is defined as "a diagram showing the relation between variable quantities." That doesn't fit the virtues and vices thingies.

Perhaps the technical definitions in math are different? 1210581870:::Steve D'Ippolito:::::::::A Venn diagram is specifically the use of overlapping (or maybe not) circles to depict sets, their intersections (the area of overlap) and unions (the combined area of the circles). I believe that mathematicians would refer to the connected dots as a "graph" even though in the wider sense of the word everything you showed is a diagram of some sort. But only the first two are specifically Venn diagrams, no matter which definition of "diagram" you use.

Of course you have a mathematician who makes house calls (and has done so for nine years, congrats!) so I should bow out at this point. 1210598456:::Mike Hardy:::hardy@math.umn.edu::::::> Mike says: "The first and second are
> Venn diagrams. The third and fourth
> are graphs."
>
> My Oxford American Dictionary defines
> a diagram as "a simplified drawing
> showing the appearance, structure, or
> workings of something; a schematic
> representation." By that definition,
> all four thingies are diagrams.

But you omitted the word "Venn". Look up "Venn diagram".

> In contrast, a graph is defined as
> "a diagram showing the relation
> between variable quantities."
> That doesn't fit the virtues and
> vices thingies.

Doesn't fit at all, but you're looking it up in the wrong book. A couple of hours ago I submitted a longish posting to ATL2 about this very point. Start with that. Maybe I'll copy that to here when I'm not as rushed.

> Perhaps the technical definitions
> in math are different?

Definitely. 1210599782:::Mike Hardy:::hardy@math.umn.edu::::::OK, this is excerpted from my ATL2 posting:

> Is there a name for that other style of graph?

In some contexts it's just called a graph, and
the term is taken to mean a bunch of dots some
of which may be connected to each other by a
line between them. In the case on Diana Hsieh's
web site, ALL of them are connected, so it's a
"complete graph". See the following:

http://en.wikipedia.org/wiki/Graph_(mathematics)
http://en.wikipedia.org/wiki/Graph_theory
http://en.wikipedia.org/wiki/List_of_graph_theory_topics

The definition posted above may make the topic
superfially appear trivial, so I'll mention some
rather deep things:

Some simple problems related to "graph coloring"
are NP-complete problems. See the following:
http://en.wikipedia.org/wiki/NP_complete
http://en.wikipedia.org/wiki/Graph_coloring

The four-color problem was an unsolved problem in
graph theory for (I think) more than a century.
(I'd be surprised if most people on this list
haven't heard of that one.):
http://en.wikipedia.org/wiki/Four-color_problem

A problem in graph theory that no one has succeeded
in solving although a fair number have valiantly
tried is found here:
http://en.wikipedia.org/wiki/Heawood_conjecture

The solution of one very difficult problem is the
Robertson-Seymour theorem:
http://en.wikipedia.org/wiki/Robertson%E2%80%93Seymour_theorem

To give examples of things that don't involve
problems whose solution would be a major breakthrough
but will definitely cost you some skull-sweat, take
a look at these:
http://en.wikipedia.org/wiki/Laplacian_matrix
http://en.wikipedia.org/wiki/Algebraic_connectivity

And here's something practical:

http://en.wikipedia.org/wiki/Expander_graph

Some very good mathematicians devote whole careers
to this topic. 1210618241:::Diana Hsieh:::diana@dianahsieh.com:::http://www.dianahsieh.com/blog:::Ah, I just realized that I did use the term "venn diagrams" in the title of the post. I forgot to change that after I added the second two non-venn diagrams. So I have changed the title of the post accordingly. The body of the post has always been correct, as all are diagrams, even though two are not venn diagrams.

Satisfied now?