In the formal language of mathematics, a network is called a graph, and graph theory is the area of mathematics that studies these objects called graphs. Graph theory is a relatively new area of mathematics that gives us a formal language with which to describe networks. The first theory of graphs goes back to 1736. The first textbook came about in 1958 but most of the work within this field is less than a few decades old. In its essence, a graph is really very simple. It consists of just two parts, what are called vertices and edges. Firstly vertices, a vertex or node is a thing, that is to say, it is an entity, and we can ascribe some value to it. So a person is an example of a node, as is a car, planet, farm, city or molecule. All of these things have static properties that can be quantified, such as the colour of our car, the size of our farm, or the weight of our molecule. Within network science vertices are more often called nodes, so we will be typically using this term during the course. Edges can be defined as a relation of some sort between two or more nodes. This connection may be tangible, as in the cables between computers on a network, or the roads between cities within a national transportation system. Or these edges may by be intangible, such as social relations of friendship. Edges may be also called links, ties or relations. The nodes belonging to an edge are called the ends, endpoints, or end vertices of the edge.

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