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Chapter 14: Problem 53

What is a weighted graph and what are the weights?

Short Answer

Expert verified
A weighted graph is a special type of graph where each edge receives a numerical value or weight. The weight could represent many different concepts based on the problem we apply the graph theory to, such as distance, cost, strength, etc.

Step by step solution

01

Understanding a Graph

A graph is a mathematical structure consisting of two components: 'vertices' or 'nodes' and 'edges'. It is used for modelling pairwise relations between objects from a certain collection. A graph can visualize relationships or connections between elements. It is used in various fields such as Physics, Computer Science, Biology, Sociology and many others.
02

Defining a Weighted Graph

A weighted graph is a special type of graph in which each edge is assigned a numerical value or 'weight'. Generally, these weights represent costs, lengths, or capacity, depending on the problem the graph is modelling. Weighted graphs are used in path-finding problems, in networking to represent bandwidth, in social networks to represent the strength of relationships, etc.
03

Understanding Weights in a Graph

The 'weights' in a graph are the numerical values associated with the edges. These values could represent many real-world concepts such as distances between two cities, cost to travel from one node to another, the strength of relationships among social entities, the capacity of a channel in networking, etc. The meaning of the weights is based on the particular problem that we apply the graph theory.

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