Weighted Graph

There is some variation in the literature but typically a weighted graph refers to an edge weighted graph that is a graph where edges have weights or values. Representing a weighted graph using an adjacency array. Such weights might represent for example costs lengths or capacities depending on the problem at hand.

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Usually the edge weights are nonnegative integers.

Weighted graph. Each edge of a graph has an associated numerical value called a weight. A set of vertices v. If there is no edge between node i and node j the value of the array element a i j some very large value otherwise a i j is a floating value that is equal to the weight of the edge i j. This number can represent many things such as a distance between 2 locations on a map or between 2 connections on a network.

A set of edges e. What is weighted graph. A weighted graph is therefore a special type of labeled graph in which the labels are numbers which are usually taken to be positive. Well colored a well colored graph is a graph all of whose greedy colorings use the same number of colors.

This module covers weighted graphs where each edge has an associated weight or number. A weighted graph or a network is a graph in which a number the weight is assigned to each edge. A graph is called weighted graph when it has weighted edges which means there are some cost associated with each edge in graph. These weighted edges can be used to compute the shortest path.

In this post weighted graph representation using stl is discussed. Weighted graphs may be either directed or undirected. Shortest path in a weighted graph where weight of an edge is 1 or 2 given a directed graph where every edge has weight as either 1 or 2 find the shortest path from a given source vertex s to a given destination vertex t. Such graphs arise in many contexts for example in shortest path problems such as the traveling salesman problem.

We use two stl containers to represent graph. Here we use it to store adjacency lists of all vertices. Expected time complexity is o v e. A weighted graph refers to a simple graph that has weighted edges.

Weighted graph a graph whose vertices or edge s have been assigned weight s. The implementation is for adjacency list representation of weighted graph. In set 1 unweighted graph is discussed. Without the qualification of weighted the graph is typically assumed to be unweighted.

A weighted graph is a graph in which each branch is given a numerical weight. More specifically a vertex weighted graph has weights on its vertices and an edge weighted graph has weights on its edges.