Graph is suddenly in fashion but not as we know it. Instead of referring to graphs when people talk about social graphs, they are now talking about sets, networks, and other systems of organisation using the terminology from a branch of mathematics called Graph theory. Graph replaced enable as the word you have to insert into your PR speeches to attract attention.
Graph theory has valid uses. Most examples do not need full blown graph theory because the information described in a network or some other simpler structure. Think of a situation where you visit your brother in law, he asks you to pin some wood on the wall, and hands you a nail. You ask for a hammer. He leads you into a giant workshop with every known machine and says
there is some wood over there, some steel over there. Graph theory can be overkill.
In the last few weeks I ran across a few interviews and Web pages using the term graph where they were talking about something simpler and I wondered why they called it a graph instead of whatever it really is. Pretentious came to mind. Some people have a need to use 12 letter words where four letters fit while others need to feel different and superior by using words not in common use, words that make people ask questions.
Graphs, of the graph theory kind, contain two things, things that may be connected, and connections. Everyone else calls the things-that-may-be-connected nodes or objects but graph theory calls them vertices. Many of the users of the term graph, use the term about collections or groups or sets of unrelated items or undefined items. Many of the may-be-connected connections are not actual connections related to the things-that-may-be-connected but are instead circumstantial adjacentments.
Hey, I invented a word and a theory, Adjacentmentation theory.
When things are adjacent, it does not mean they are related. You might find an airplane jet engine next to a car. That does not imply a relationship between the jet engine and the car. The number of cars using jet engines is truly trivial, perhaps only three in the whole world. The adjacentment is more likely to be due to the car being parked near an airport and the engine is on a truck on the way to a repair shop, or the car is anywhere and the engine fell out of an airplane, something we can expect more of now that QANTAS is outsourcing maintenance to the cheapest places on the planet.
One misuse of adjacentmentation was in a description of the Facebook equivalent to groups, something Facebook is not good at. (Facebook lists are the closest you can get and Facebook lists are really only equivalent to Google circles, not groups, not Drupal groups, not Google groups, not any groups.
In a Facebook pretend group, you can be there because someone else added you without your permission. That places you in the group without being a member of the group. You happen to be adjacent to someone who is in the group and they wanted to brag about the number of people they know so they threw you in but you are not really a member of the group. You are there by adjacementarianism.
Graph theory would just invent a new type of relationship to make you a member of the group. Outside of graph theory, where people live and work, the relationship would be a network through the annoying friend who added you without your consent and without the consent of the group. In data architecture, the relationship would be marked as
error and the software that let the relationship into the data base would be labelled
In the Facebook case, the result is so many people leaving Facebook for anything else, that in some months the number of people using Facebook goes down instead of up.
The term edge suggests edge cases and a whole bunch of other things. In Graph theory an edge is not an edge, an edge is a connection between objects, or nodes, with, in some cases, the edge going out to something undefined or not included.
Some people try to define a graph as different from a tree structure based on the type of connection but every type of connection used in a graph is valid in a tree. If the tree does not fit a standard tree structure because it does not have a starting point, the structure is a network.
Does graph theory provide an explanation>
I have yet to find a use of graph theory where graph theory provides the only valid explanation of something. In most cases, graph theory leads to complicated discussions that lead only to more complicated discussions. The explanation of the original observation is usually far easier.
Graph is misused the way fashion victims misused the word
irony many years ago. You do not have to call something a graph if it is not a visual representation or something so complex that it needs graph theory to explain.