Welcome to Graph Theory

In the coming 12 weeks we will be investigating what we can do with what mathematicians call graphs. The concept of a graph in itself is very simple: we take any finite set of things (which we'll call vertices) and describe how those edges can be connected by what we call vertices, in other words we'll specify some sets consisting of 2 vertices: Here's an example of a graph on 8 vertices:

so that
Graph theory is the mathematical language to study interconnectedness
In other words graph, being very basic gadgets are capable of describing an immensely wide variety of phenomena. A large part of week 1 will be dedicated to describing the typical problems problems of the field (and going over the original problem that started it all, the Konigsberg puzzle).

In the second week move on to investigate a few properties of graphs and obtain some quick and easy results that give a description of certain types of graphs