Graphs in mathematics

A graph is a mathematical structure of objects in which some pairs of objects are connected by links. The objects are denoted by abstractions called nodes (also known as vertices) and their links are represented by relationships (also known as edges). The relationships might be directed where it makes semantic sense in one particular direction. In cases where the semantics work in both directions, we can safely use undirected relationships to denote the link.

Figure 1.1: Edges, vertices, directionality

In Figure 1.1, we have three actors or entities, Alice, Bob, and London, which are represented as nodes. The links between them are denoted by relationships. Alice is married to Bob and Bob is married to Alice. Both true, hence we represent Is Married To as an undirected relationship. However, Alice lives in London is represented by a directed relationship, Lives In, from Alice to London. This is because London lives in Alice cannot be true.