JOUR 601 Lecture Notes - Lecture 31: Graph Theory, Network Science, Glossary Of Graph Theory Terms
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Graph Theory Overview
When we think of networks, we may think of social networks and the internet.
Forget about what you think you know about networks and embrace the abstract language of
In mathematics, a network is called a graph. Graph theory is the area of mathematics that
The first concept of this theory dates back to 1736. However, most of the work within this field
is less than 20-30 years old.
Graph: consists of two parts, vertices and edges.
Vertices: A vertex or node is a thing or entity described with some value to it. For example, a
person, car, planet, farm, city, etc.
All nodes have static properties that can be quantified. For example, the color of our car, the
weight of the person, etc.
In network science, vertices are mostly called nodes, so when you see nodes, know it is
referring to a vertices that has a quantifiable measure.
Edges: a tangible or intangible relation of some sort between two nodes.
An example of a tangible relationship is the relationship of roads between cities in a nation’s
An example of an intangible relationship is a social relation or friendship.
Edges are also referred to as links, ties, or relations. More often, we use these terms.
The nodes that belong to an edge are called the end points, ends, or end vertices of the edge.
Within graph theory, networks are referred to constantly as graphs. A graph is defined as a set
of edges and a set of vertices.
Knowing these two points, it is important to note that a simple graph does not contain loops or
As an example, a simple graph would tell us whether there is a connection between to cities.
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