Mastering Machine Learning with Spark 2.x

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 is, e_i = (v₁, v₂). Let's construct a simple graph consisting of five vertices and six edges, as specified by the following graph data:

V ={v₁, v₂, v₃, v₄, v₅}

E = {e₁ = (v₁, v₂), e₂ = (v₁, v₃), e₃ = (v₂, v₃),

       e₄ = (v₃, v₄), e₅ = (v₄, v₁), e₆ = (v₄, v₅)}

This is what the graph will look like:

Figure 1: A simple undirected graph with five vertices and six ...