Basic Definitions of Network

Network

Basic Definitions

A graph, or network, is defined by two sets of symbols: nodes and arcs. First, we define a set (call it V) of points, or vertices. The vertices of a graph or network are also called nodes.

Definition) An arc consists of an ordered pair of vertices and represents a possible direction of motion that may occur between vertices.

Definition) A sequence of arcs such that every arc has exactly one vertex in common with the previous arc is called a chain.

Definition) A path is a chain in which the terminal node of each arc is identical to the initial node of the next arc.

from. Introduction to Mathematical Programming (4th Edition), Wayne L. Winston, Munirpallam Venkataramanan, Thomson Brooks/Cole, 2002.