Formalizing graphs
Graphs are a very popular concept in mathematics. In this domain, a common terminology is well accepted. Let’s take a closer look.
Definition and semantics
With the argument being made for graph representations to be a relevant topic for practical problems, let’s take a moment to define what a graph is. A graph is an abstract concept. Mathematically, it’s generally represented as 
, where 
is the graph, which contains a set of vertices, 
, and a set of edges, 
. Each element of is a tuple, 
, where 
, and represents a connection between the two vertices. That’s all there is to the mathematical definition; how you choose to apply semantics to this is completely up to you.
In the example mentioned in the previous section, the users of the social media platform were represented by the vertices, and the connection between the two users was represented by the edges. Also, vertices and edges need not be so homogeneous. Consider the graph...
