Basic graph theory

Before diving into Spark GraphX and its applications, we will first define graphs on a basic level and explain what properties they may come with and what structures are worth studying in our context. Along the way of introducing these properties, we will give more concrete examples of graphs that we consider in everyday life.

Graphs

To formalize the notion of a graph briefly sketched in the introduction, on a purely mathematical level, a graph G = (V, E) can be described as a pair of vertices V and edges E, as follows:

V = {v₁, ..., v_n}

E = {e₁, ..., e_m}

We call the element v_i in V a vertex and e_i in E an edge, where each edge connecting two vertices v₁ and v₂ is, in fact, just a pair of vertices, that...