Ninth Week

Network or Graph Theory

A graph is defined as a set of edges and a set of vertices. A multi-graph is a graph with multiple edges between the nodes. 

Undirected graphs include two nodes with an edge that does not indicate directionality -- an unordered pair (Jane is married to Paul. Paul is married to Jane). 

Directed graphs include edges which do indicate clear directionality (flow and order). Edges in a directed graph may be weighted, in that certain edges are given a weighted number (for example $100 million in import/ $150 million in export).

Multiplex Networks capture how different networks interrelate and overlap to effect each other. 

Vertices 

• Vertexes are things (nodes).

• All nodes (things like people, molecules, objects) have properties that can be quantified.

Edges

• Edges are a relation of some sort between two nodes.

• This connection or relation between nodes can be physical (like underwater cables physically connecting networks or roads between cities) or intangible (like social relationships).

• Edges are also known as links, ties, or relations,

• The nodes belonging to an edge are called the ends, endpoints, or end vertices.

(Systems Innovation, April 18, 2015)