# Weighted graph matrix representation pdf

Create graph and find the shortest path. On the Help page you will find tutorial video. Multigraph matrix contains weight of minimum edges between vertices. Matrix is incorrect. Use comma "," as separator. Matrix should be square. Graph was saved. Follow this link to see it. Open image in browser or Download saved image. Our service already supports these features: Find the shortest path using Dijkstra's algorithmAdjacency matrixIncidence Matrix.

Click to workspace to add a new vertex. Vertex enumeration. Select the initial vertex of the shortest path. The number of weakly connected components is. Toggle navigation Graph Online. Find shortest path Create graph and find the shortest path. Create algorithm Paste your algorith below and press Run.

Enter title Group rename. Enter text for each vertex in separate line. Setup adjacency matrix. Use comma "," as separator Multigraph matrix contains weight of minimum edges between vertices.

Set up incidence matrix. Matrix of minimal distances. Share link in social networks:. Open image in browser or Download saved image Share link in social networks:. Your algorithm was sent to check and in success case it will be add to site. Cannot create graph. Adjacency Matrix has wrong format. Click "fix matrix" button to fix matrix or "help" button to open help about Adjacency Matrix format.

Incidence Matrix has wrong format. Click "fix matrix" button to fix matrix or "help" button to open help about Incidence Matrix format. What functions should we add firstly? Search longest path on graph. Depth-first search and breadth-first search.

Search all paths from vertex A to vertex B.In Set 1unweighted graph is discussed. In this post, weighted graph representation using STL is discussed. The implementation is for adjacency list representation of weighted graph. This article is contributed by Sahil Chhabra akku. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.

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Please use ide. We use two STL containers to represent graph:. The program basically prints adjacency list. Recommended Posts: Graph implementation using STL for competitive programming Set 1 DFS of Unweighted and Undirected Prefix Sum Array - Implementation and Applications in Competitive Programming Shortest Path in a weighted Graph where weight of an edge is 1 or 2 Shortest path with exactly k edges in a directed and weighted graph Set 2 Shortest path with exactly k edges in a directed and weighted graph Implementation of Graph in JavaScript Convert the undirected graph into directed graph such that there is no path of length greater than 1 Maximum number of edges that N-vertex graph can have such that graph is Triangle free Mantel's Theorem Detect cycle in the graph using degrees of nodes of graph Tips and Tricks for Competitive Programmers Set 2 Language to be used for Competitive Programming Longest path in a directed Acyclic graph Dynamic Programming How can competitive programming help you get a job?

How to begin with Competitive Programming? How to become a master in competitive programming? Python in Competitive Programming. Improved By : Ritesh Ghorse. Load Comments.There are two principal ways to represent a graph G with the matrix, i. Solution: Since graph G consist of four vertices. Therefore, the adjacency matrix wills a 4 x 4 matrix. The adjacency matrix is as follows in fig:. The number of ones in an incidence matrix of the undirected graph without loops is equal to the sum of the degrees of all the vertices in a graph.

Example: Consider the undirected graph G as shown in fig. Find its incidence matrix M I. Solution: The undirected graph consists of four vertices and five edges.

Therefore, the incidence matrix is an 4 x 5 matrix, which is shown in Fig:. Example: Consider the directed graph shown in fig. Determine its adjacency matrix M A. Solution: Since the directed graph G consists of five vertices. Therefore, the adjacency matrix will be a 5 x 5 matrix. The adjacency matrix of the directed graphs is as follows:.

Example: Consider the directed graph G as shown in fig. Solution: The directed graph consists of four vertices and five edges. Therefore, the incidence matrix is a 4 x 5 matrix which is show in fig:.

Solution: Since the multigraph consist of five vertices. Therefore the adjacency matrix will be an 5 x 5 matrix. The adjacency matrix of the multigraph is as follows:. JavaTpoint offers too many high quality services. Mail us on hr javatpoint. Please mail your requirement at hr javatpoint. Duration: 1 week to 2 week. Discrete Mathematics. Binary Operation Property of Binary Operations. Next Topic Isomorphic and Homeomorphic Graphs. Spring Boot.

Selenium Py. Verbal A. Angular 7. Compiler D. Software E.By Graph representation, we simply mean the technique which is to be used in order to store some graph into the computer's memory. There are two ways to store Graph into the computer's memory. In this part of this tutorial, we discuss each one of them in detail. In sequential representation, we use adjacency matrix to store the mapping represented by vertices and edges. In adjacency matrix, the rows and columns are represented by the graph vertices.

A graph having n vertices, will have a dimension n x n. An entry M ij in the adjacency matrix representation of an undirected graph G will be 1 if there exists an edge between V i and V j.

There exists different adjacency matrices for the directed and undirected graph. In directed graph, an entry A ij will be 1 only when there is an edge directed from V i to V j.

Representation of weighted directed graph is different. Instead of filling the entry by 1, the Non- zero entries of the adjacency matrix are represented by the weight of respective edges. The weighted directed graph along with the adjacency matrix representation is shown in the following figure. In the linked representation, an adjacency list is used to store the Graph into the computer's memory. Consider the undirected graph shown in the following figure and check the adjacency list representation.

An adjacency list is maintained for each node present in the graph which stores the node value and a pointer to the next adjacent node to the respective node. If all the adjacent nodes are traversed then store the NULL in the pointer field of last node of the list. The sum of the lengths of adjacency lists is equal to the twice of the number of edges present in an undirected graph.

Consider the directed graph shown in the following figure and check the adjacency list representation of the graph. In a directed graph, the sum of lengths of all the adjacency lists is equal to the number of edges present in the graph.

In the case of weighted directed graph, each node contains an extra field that is called the weight of the node. The adjacency list representation of a directed graph is shown in the following figure. JavaTpoint offers too many high quality services.

Mail us on hr javatpoint. Please mail your requirement at hr javatpoint. Duration: 1 week to 2 week. DS Tutorial. DS Array 2D Array. Linear Search Binary Search. Spring Boot. Selenium Py. Verbal A. Angular 7. Compiler D. Software E. Web Tech. Cyber Sec. Control S. Data Mining. Javatpoint Services JavaTpoint offers too many high quality services. Sequential Representation In sequential representation, we use adjacency matrix to store the mapping represented by vertices and edges.Graph is a data structure that consists of following two components: 1.

A finite set of vertices also called as nodes. A finite set of ordered pair of the form u, v called as edge. The pair is ordered because u, v is not same as v, u in case of a directed graph di-graph. The pair of the form u, v indicates that there is an edge from vertex u to vertex v.

Graphs are used to represent many real-life applications: Graphs are used to represent networks. The networks may include paths in a city or telephone network or circuit network. Graphs are also used in social networks like linkedIn, Facebook. For example, in Facebook, each person is represented with a vertex or node.

Each node is a structure and contains information like person id, name, gender and locale. See this for more applications of graph. Following is an example of an undirected graph with 5 vertices. Following two are the most commonly used representations of a graph. Adjacency Matrix 2.

The choice of the graph representation is situation specific. It totally depends on the type of operations to be performed and ease of use. Adjacency matrix for undirected graph is always symmetric. Adjacency Matrix is also used to represent weighted graphs. The adjacency matrix for the above example graph is:. Pros: Representation is easier to implement and follow. Removing an edge takes O 1 time.

Even if the graph is sparse contains less number of edgesit consumes the same space. Please see this for a sample Python implementation of adjacency matrix. Adjacency List: An array of lists is used. Size of the array is equal to the number of vertices. Let the array be array[].

An entry array[i] represents the list of vertices adjacent to the i th vertex.There are several different ways to represent a graph in a computer. Although graphs are usually shown diagrammatically, this is only possible when the number of vertices and edges is reasonably small. Graphs can also be represented in the form of matrices. The major advantage of matrix representation is that the calculation of paths and cycles can easily be performed using well known operations of matrices.

However, the disadvantage is that this form of representation takes away from the visual aspect of graphs. It would be difficult to illustrate in a matrix, properties that are easily illustrated graphically. Consider the following directed graph G in which the vertices are ordered as v 1v 2v 3v 4and v 5and its equivalent adjacency matrix representation on the right:. As you can see from the above graph, if a path of length 1 exists from one vertex to another ie.

For example, from the vertex v1, we can reach vertices v2, v4, and v5. Therefore, we have a corresponding entry of 1 in the matrix in the first row and the second, fourth and fifth columns. In general, the number of 1's in the ith row, corresponds to the number of edges leaving the vertex v iand the number of 1's in the jth column, corresponds to the number of edges entering the vertex v j. An adjacency matrix is defined as follows: Let G be a graph with "n" vertices that are assumed to be ordered from v 1 to v n.

The n x n matrix A, in which. As shown in the previous example, the existence of an edge between two vertices v i and v j is shown by an entry of 1 in the i th row and j th column of the adjacency matrix. This entry represents a path of length 1 from v i to v j.

To compute a path of length 2, the matrix of length 1 must be multiplied by itself, and the product matrix is the matrix representation of path of length 2. Using the matrix from the previous example and multiplying it by itself, we obtain the following new matrix:. The above matrix indicates that we can go from vertex v1 to vertex v2, or from vertex v1 to vertex v4 in two moves.

In fact, if we examine the graph, we can see that this can be done by going through vertex v5 and through vertex v2 respectively. We can also reach vertex v2 from v3, and vertex v4 from v5, all in two moves. In general, to generate the matrix of path of length n, take the matrix of path of length n-1, and multiply it with the matrix of path of length 1. Click here to see how matrix multiplication is done. Click here to see an interactive example of an Adjacency Matrix. Or move on to the next page to go directly to the next section.

Original Graph G:. Matrix representation of path of length 2.The two vertices are called the edge endpoints. Graphs are ubiquitous in computer science. They are used to model real-world systems such as the Internet each node represents a router and each edge represents a connection between routers ; airline connections each node is an airport and each edge is a flight ; or a city road network each node represents an intersection and each edge represents a block.

The wireframe drawings in computer graphics are another example of graphs. A graph may be either undirected or directed.

## Graphs - Terminology and Representation

Intuitively, an undirected edge models a "two-way" or "duplex" connection between its endpoints, while a directed edge is a one-way connection, and is typically drawn as an arrow. A directed edge is often called an arc. Mathematically, an undirected edge is an unordered pair of vertices, and an arc is an ordered pair.

For example, a road network might be modeled as a directed graph, with one-way streets indicated by an arrow between endpoints in the appropriate direction, and two-way streets shown by a pair of parallel directed edges going both directions between the endpoints.

You might ask, why not use a single undirected edge for a two-way street. There's no theoretical problem with this, but from a practical programming standpoint, it's generally simpler and less error-prone to stick with all directed or all undirected edges. A multigraph can have more than one edge between the same two vertices. For example, if one were modeling airline flights, there might be multiple flights between two cities, occurring at different times of the day.

An undirected acyclic graph is equivalent to an undirected tree. A directed acyclic graph is called a DAG. It is not necessarily a tree. Nodes and edges often have associated information, such as labels or weights. For example, in a graph of airline flights, a node might be labeled with the name of the corresponding airport, and an edge might have a weight equal to the flight time.

The popular game " Six Degrees of Kevin Bacon " can be modeled by a labeled undirected graph. Each actor becomes a node, labeled by the actor's name. Nodes are connected by an edge when the two actors appeared together in some movie. We can label this edge by the name of the movie. Deciding if an actor is separated from Kevin Bacon by six or fewer steps is equivalent to finding a path of length at most six in the graph between Bacon's vertex and the other actors vertex.

This can be done with the breadth-first search algorithm found in the companion Algorithms book. The Oracle of Bacon at the University of Virginia has actually implemented this algorithm and can tell you the path from any actor to Kevin Bacon in a few clicks . The number of edges with one endpoint on a given vertex is called that vertex's degree. In a directed graph, the number of edges that point to a given vertex is called its in-degreeand the number that point from it is called its out-degree. Often, we may want to be able to distinguish between different nodes and edges. We can associate labels with either.

We call such a graph labeled. To do: also need undirected graph abstraction in that section, and also find a better set of operations-- the key to finding good operations is seeing what the algorithms that use graphs actually need.