Skip to main content

Basics of Graph Theory

Graph Theory is the study of relationships in graphs along with graphs in general. A graph is made up of nodes (points on the graph) and edges (connections between those nodes). Graphs are abstract data types used from making maps to social networks, to finding an actor's bacon number. In the example of Facebook, the nodes would be the users on the network and when two users become friends, a connection (edge) is formed.
Example graph

A graph can be a simple graph or a multigraph. A simple graph has one type of edge while a multigraph can multiple types of edges.

For example consider the graph below which shows the bike paths between of paths between buildings.

This would be a simple graph because the only type of edge would be the bike paths. However, imagine if we also wanted to consider skateboard paths.


Some paths may be bike paths, some may be skateboard paths and some may be both! In the multigraph above we can represent all 3 types.

Graphs are resourceful in that they can represent different types of data and be applied to many different situations which still being able to organize the data in a coherent manner. The structure of a graph allows for abstract representations that range from transportation to actor databases which make them a valuable resource as a data type.

Popular posts from this blog

Compiled vs Interpreted

Do you program? Do you write code? Depending on what you're programming or trying to create, you'll need a programming language and depending on the task at hand the decision will need to be made of using an interpreted or compiled language.

What's the difference?

Think about it like this, when you read a book, you read it line by line. An interpreted language does the same kind of thing. It reads the code in a file line by line. Immediately after that line is read, the program reading the code (the interpreter) runs that line of code then moves on to the next one. This is typically done for platforms such as the web.

A compiled language is slightly different. A compiled language would read the entire file of code, and translate it to another format (ex. machine code or another language). This is done by a compiler. Once the code is in another format it can be run. These types of languages are usually used for native desktop or mobile applications.

There is a mix of interprete…
Read more

So what is Machine Learning?

It’s mentioned all the time in the news and companies are constantly touting how enhanced their applications are with learning machines. But what does that really mean?
To put it simply, its teaching a machine how to do something. There’s more than one way to do this but most models follow the same method of “Practice makes perfect”.
For example, if I wanted to learn how to draw, I would start with the basics and do simple things. I would practice the motions and gestures that I wanted to get the desired effect. The more I practice, the better (in most cases) I would get. My skill would improve over time. However I could be learning the wrong way and actually be making my drawing ability worse.
Teaching machines is the same way. A machine is given a data set (ex. a series of images it wants to learn how to draw) and it runs a loop that practices its skill at finding patterns amongst the data set (ex. a flower petal is more curves than straight lines, while a sidewalk is mostly straig…
Read more