## What is a weighted graph in data structure?

A weighted graph refers to one where weights are assigned to each edge. Weighted graphs can be represented in two ways: Directed graphs where the edges have arrows that show path direction. Undirected graphs where edges are bi-directional and have no arrows.

## What is meaning of weighted graph?

A weighted graph is a directed graph in which all nodes have an integer weight.

**What is a multiple graph?**

In mathematics, and more specifically in graph theory, a multigraph is a graph which is permitted to have multiple edges (also called parallel edges), that is, edges that have the same end nodes. Thus two vertices may be connected by more than one edge.

### What is multi graph in discrete structure?

Multi-graph: A graph in which there are multiple edges between any pair of vertices or there are edges from a vertex to itself, also called a loop. Planar graph: A graph that can be drawn so that all of the edges of the graph do not cross each other.

### What is simple graph and multiple graph?

Simple graphs have their nodes connected by only one link type, such as road or rail links. A multigraph can contain more than one link type between the same two nodes.

**What is a multi graph illustrate an example?**

When multiple edges are allowed between any pair of vertices, the graph is called a multigraph. Examples of a simple graph, a multigraph and a graph with loop are shown in Figure 8.9. Figure 8.9. Examples of (a) simple graph, (b) multigraph, and (c) graph with loop.

## What is multistage graph problem?

The multistage graph problem is to find a minimum cost from a source to a sink. A multistage graph is a directed graph having a number of multiple stages, where stages element should be connected consecutively. In this multiple stage graph, there is a vertex whose in degree is 0 that is known as the source.

## Which is the application of weighted graph?

Weighted graphs may be either directed or undirected. The weight of an edge is often referred to as the “cost” of the edge. In applications, the weight may be a measure of the length of a route, the capacity of a line, the energy required to move between locations along a route, etc.

**What is weighted graph in discrete mathematics?**

Weighted graph: A graph in which weights, or numerical values, are assigned to each of the edges. Mary’s graph is a weighted graph, where the distances between the cities are the weights of the edges.

### What is multistage graph in design and analysis of algorithm?

A multistage graph G = (V, E) is a directed graph where vertices are partitioned into k (where k > 1) number of disjoint subsets S = {s1,s2,…,sk} such that edge (u, v) is in E, then u Є si and v Є s1 + 1 for some subsets in the partition and |s1| = |sk| = 1.

### What is the time complexity of multistage graph?

Time complexity of Multistage Graph is O(n^2) or O(v^2) but then some people says it’s O(E). So, from O(V^2) to O(E) are they taking about dense/complete graphs in which number of edges |E| = |V^2|?

**What is multistage graph problem solving using dynamic programming?**