Advantages and disadvantages of using adjacency list over adjacency matrix? Graphs Implementation Tips Adjacency lists have the advantage of being more from ECE 250 at University of Waterloo *Response times vary by subject and question complexity. Explain which is best and why? There are 2 big differences between adjacency list and matrix. Which of the following is an advantage of adjacency list representation over adjacency matrix representation of a graph? 's book, or StackOverFlow : Size of a graph using adjacency list versus adjacency matrix? Tom Hanks, Kevin Bacon As mentioned earlier, we may represent graphs using several methods. Graphs out in the wild usually don't have too many connections and this is the major reason why adjacency lists are the better choice for most tasks.. In this tutorial, we will cover both of these graph representation along with how to implement them. Adjacent list allows us to store graph in more compact form, than adjacency matrix, but the difference decreasing as a graph becomes denser. One is space requirement, and the other is access time. An adjacency list uses less storage to store a graph if there are many vertices with few edges for each vertex. Which of the following is an advantage of adjacency list representation over adjacency matrix representation of a graph? Advantages of an adjacency matrix. Sparse Graphs. understand about Genetics Algorithms ? In this post, we discuss how to store them inside the computer. There are several other ways like incidence matrix, etc. Find answers to questions asked by student like you. as quickly as an adjacency matrix. Given a graph, to build the adjacency matrix, we need to create a square matrix and fill its values with 0 and 1. In an adjacency list implementation we keep a master list of all the vertices in the Graph object and then each vertex object in the graph maintains a list … These operations take O(V^2) time in adjacency matrix representation. Median response time is 34 minutes and may be longer for new subjects. An adjacency list representation for a graph associates each vertex in the graph with the collection of its neighboring vertices or edges. List? The C++ program illustrates the concept of constructor. So we can see that in an adjacency matrix, we're going to have the most space because that matrix can become huge. Wiki User Answered . In the transpose graph, add u to adjacency list of v (there exists and edge from v to u i.e. Adjacency Matrix or Adjacency List? Adjacency Matrix: Adjacency Matrix is a 2D array of size V x V where V is the number of vertices in a graph. Show the breadth-first search tree with S as the source. The adjacency matrix of an undirected graph can also be represented in the form of an array. Which of the following is an advantage of adjacency list representation over adjacency matrix representation of a graph? Give the adjacency matrix representation of Q 3, numbering the vertices in the obvious order. LIST the advantages and disadvantages of using plastic? In a weighted graph, the edges Give the adjacency matrix for K 4. Then, values are filled in to the matrix to indicate if there is or is not an edge between every pair of nodes. generate link and share the link here. Q: Describe the need for an array when processing items that are thesame data type and represent the sa... A: The first three questions will be answered. B DFS and BSF can be done in O(V + E) time for adjacency list representation. This method is widely employed to represent graphs. Describe what the adjacency matrix looks like for K n for n > 1. Assuming the graph has vertices, the time complexity to build such a matrix is .The space complexity is also . Adjacency list 1. or Wikipedia. 8.5. A In adjacency list representation, space is saved for sparse graphs. Advantages Disadvantages Adjacency Matrix 1) In Adjacency matrix , addition or removal of an edge can be done in linear time i.e O(1). (C) Adding a vertex in adjacency list representation is easier than adjacency matrix representation. Dijkstra algorithm is a greedy algorithm. Adjacency List. Experience. Once in the adjacency list of either end of the edge. Each list corresponds to a vertex u and contains a list of edges (u;v) that originate from u. Problem 10.8. See the example below, the Adjacency matrix for the graph shown above. (D) All of the above Dense graph Sparse graph Adjacency list is always preferred None of the mentioned. A directory of Objective Type Questions covering … A. Unanswered Questions. Which of the following is an advantage of adjacency list representation over adjacency matrix representation of a graph? For example, the adjacency list for the Apollo 13 network is as follows: Tom Hanks, Bill Paxton. In a binary search tree a node must be s... Q: Q2  A genetic algorithm is a search heuristic that is inspired by Charles Darwin'... Q: You have to write a C++ Program to store temperature of four different cities for a week. (A) In adjacency list representation, space is saved for sparse graphs. An alternative to the adjacency list is an adjacency matrix. Adjacency Matrix is also used to represent weighted graphs. 2) It is very simple to work and … (B) DFS and BSF can be done in O(V + E) time for adjacency list representation. Say, the node is u, now traverse each node in the adjacency list of u. What property does the adjacency matrix of every undirected graph have that Implementation of DFS using adjacency matrix Depth First Search (DFS) has been discussed before as well which uses adjacency list for the graph representation. A: For two parties, A and B, the main approaches to distribution can be accomplished in a variety of wa... Q: what do you An adjacency list is more space efficient. See Answer. Data Structures and Algorithms Objective type Questions and Answers. Give 3 uses for trees. Given a graph, to build the adjacency matrix, we need to create a square matrix and fill its values with 0 and 1. The time complexity for this case will be O(V) + O (2E) ~ O(V + E). Usually easier to implement and perform lookup than an adjacency list. In adjacency matrix representation, memory used to represent graph is O(v 2). Adjacency List; Adjacency Matrix: Adjacency Matrix is 2-Dimensional Array which has the size VxV, where V are the number of vertices in the graph. These operations take O(V^2) time in adjacency matrix representation. A. An adjacency matrix is a matrix where both dimensions equal the number of nodes in our graph and each cell can either have the value 0 or 1. In the previous post, we introduced the concept of graphs. Figure 1: Adjacency Matrix Representation of a Directed Graph. It costs us space.. To fill every value of the matrix we need to check if there is an edge between every pair of vertices. An Adjacency List¶. but these two are most commonly used. It shall a... A: The program prompts the user to enter temperature for 4 cities for a week and is stored in an array ... Q: Part-4: Java FX 1). Assuming the graph has vertices, the time complexity to build such a matrix is .The space complexity is also . Each edge in the network is indicated by listing the pair of nodes that are connected. These operations take O(V^2) time in adjacency matrix representation. Advantages and disadvantages of using adjacency list over adjacency matrix? Adjacency Matrix vs. So transpose of the adjacency matrix is the same as the original. Which of the following is an advantage of adjacency list representation over adjacency matrix representation of a graph? Tom Hanks, Gary Sinise. Refer to Graph and its representations for the explaination of Adjacency matrix and list. v -> u). Such places include Cormen et al. We, with the adjacency sets implementation, have the same advantage that the adjacency matrix has here: constant-time edge checks. Describe how Lamport’s algorithm maintains a global... A: An algorithm which is known as lamport's algorithm which will show us that it is possible to receive... Q: Linux: The command that can be used to mount all filesystems listed in /etc/fstab except those conta... *Response times vary by subject and question complexity. Adjacency List; Adjacency Matrix: Adjacency Matrix is 2-Dimensional Array which has the size VxV, where V are the number of vertices in the graph. The adjacency list also allows us to easily find all the links that are directly connected to a particular vertex. B. DFS and BSF can be done in O(V + E) time for adjacency list representation. Asked By Wiki User. In adjacency list representation, space is saved for sparse graphs. First of all you've understand that we use mostly adjacency list for simple algorithms, but remember adjacency matrix is also equally (or more) important. 17.4 Adjacency-Lists Representation. 14, 10, 17, 12, 10, 11, 20, 12, 18, 25, 20, 8,... A: The above are the Binary search tree for the given question The primary advantage of the adjacency-lists representation over the adjacency-matrix representation is that it always uses space proportional to E + V , as opposed to V 2 in the adjacency matrix. In which case adjacency list is preferred in front of an adjacency matrix? Traverse adjacency list of each node of the graph. In an adjacency list implementation we keep a master list of all the vertices in the Graph object and then each vertex object in the graph maintains a list … Top Answer. Next advantage is that adjacent list allows to get the list of adjacent vertices in O(1) time, which is a big advantage for some algorithms. So the amount of space that's required is going to be n plus m for the edge list and the implementation list. B. DFS and BSF can be done in O(V + E) time for adjacency list representation. What is Competitive Programming and How to Prepare for It? By using our site, you Adjacency lists, in … In adjacency list representation, space is saved for sparse graphs. Tom Hanks, Gary Sinise. (B) DFS and BSF can be done in O(V + E) time for adjacency list representation. For example, the adjacency list for the Apollo 13 network is as follows: Tom Hanks, Bill Paxton. The advantage of the adjacency matrix is that it is simple, and for small graphs it is easy to see which nodes are connected to other nodes. It costs us space.. To fill every value of the matrix we need to check if there is an edge between every pair of vertices. 3 4 5. When the graph is undirected tree then Adjacency matrix: \$O(n^2)\$ Adjacency list: \$O(n + n)\$ is \$O(n)\$ (better than \$n^2\$) These operations take O(V^2) time in adjacency matrix representation. In terms of space complexity Adjacency matrix: \$O(n^2)\$ Adjacency list: \$O(n + m)\$ where \$n\$ is the number nodes, \$m\$ is the number of edges. Then there is no advantage of using adjacency list over matrix. ... -Using a static 2D array, it is harder to delete and add nodes. Adjacency Matrix An adjacency matrix is a jVjj Vjmatrix of bits where element (i;j) is 1 if and only if the edge (v i;v j) is in E. Adjacency matrix, we don't need n plus m, we actually need n squared time, wherein adjacency list requires n plus m time. Edge (also called an arc) is another fundamental part of a graph. In adjacency matrix representation, memory used to represent graph is O(v 2). Trivial Graphs: The adjacency matrix of an entire graph contains all ones except along the diagonal where there are only zeros. An adjacency list, also called an edge list, is one of the most basic and frequently used representations of a network. So we can save half the space when representing an undirected graph using adjacency matrix. b.Give one advantage that each representation has over the other. • Dense graph: lots of edges. Please use ide.geeksforgeeks.org, An adjacency list, also called an edge list, is one of the most basic and frequently used representations of a network. To learn more … acknowledge that you have read and understood our, GATE CS Original Papers and Official Keys, ISRO CS Original Papers and Official Keys, ISRO CS Syllabus for Scientist/Engineer Exam, Data Structures | Linked List | Question 4, Data Structures | Linked List | Question 5, Data Structures | Linked List | Question 6, Data Structures | Linked List | Question 7, Data Structures | Linked List | Question 8, Data Structures | Linked List | Question 9, Data Structures | Linked List | Question 10, Data Structures | Linked List | Question 11, Data Structures | Linked List | Question 13, Data Structures | Linked List | Question 14, Data Structures | Linked List | Question 15, Difference between Stack and Queue Data Structures. A more space-efficient way to implement a sparsely connected graph is to use an adjacency list. Adjacency Lists. Median response time is 34 minutes and may be longer for new subjects. 2010-05-20 09:49:54. GRAPHS Adjacency Lists Reporters: Group 10 2. Adjacency List An adjacency list is a list of lists. Both these have their advantages and disadvantages. If e is large then due to overhead of maintaining pointers, adjacency list … • The matrix always uses Θ(v2) memory. *Response times vary by subject and question complexity. It is a platform independent. These operations take O(V^2) time in adjacency matrix representation.   It connects two vertices to show that there is a … For an undirected graph with n vertices and e edges, total number of nodes will be n + 2e. There are several disadvantages. The standard representation that is preferred for graphs that are not dense is called the adjacency-lists representation, where we keep track of all the vertices connected to each vertex on a linked list that is associated with that vertex. In an adjacency matrix, a grid is set up that lists all the nodes on both the X-axis (horizontal) and the Y-axis (vertical). Advantages There are two popular data structures we use to represent graph: (i) Adjacency List and (ii) Adjacency Matrix. Which of the following is an advantage of adjacency list representation over adjacency matrix representation of a graph? Let us first have a look at the advantages and disadvantages of using this method. Here is V and E are number of vertices and edges respectively. Adjacency Matrix Definition. 8.5. Each edge in the network is indicated by listing the pair of nodes that are connected. 1 Need for an array when processing items that are the s... A: Introduction of the Program: What is the advantage of using an adjacency list over and adjacency matrix? 3. Adjacency List Approach. A. Median response time is 34 minutes and may be longer for new subjects. Q: Describe the need for an array when processing items that are thesame data type and represent the sa... A: The first three questions will be answered. Cons of adjacency matrix. Q: Construct the binary search tree of the following: While basic operations are easy, operations like inEdges and outEdges are expensive when using the adjacency matrix representation. The advantage of the adjacency list implementation is that it allows us to compactly represent a sparse graph. u -> v) . what are the advantages of an adjacency list over an adjacency matrix, Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*. Q: Describe the need for an array when processing items that are thesame data type and represent the sa... A: The first three questions will be answered. A constructor i... Q: List the different approaches of key distribution. Data Structures | Binary Search Trees | Question 8, https://www.geeksforgeeks.org/graph-and-its-representations/, C program to implement Adjacency Matrix of a given Graph, FIFO (First-In-First-Out) approach in Programming, Data Structures | Tree Traversals | Question 4, Difference between Singly linked list and Doubly linked list, Write Interview (A) In adjacency list representation, space is saved for sparse graphs. Adjacency List of node '0' -> 1 -> 3 Adjacency List of node '1' -> 0 -> 2 -> 3 Adjacency List of node '2' -> 1 -> 3 Adjacency List of node '3' -> 0 -> 1 -> 2 -> 4 Adjacency List of node '4' -> 3 Analysis . It finds a shortest path tree for a weighted undirected graph. So the amount of space that's required is going to be n plus m for the edge list and the implementation list. The amount of such pairs of given vertices is . adjMaxtrix[i][j] = 1 when there is edge between Vertex i and Vertex j, else 0. • The adjacency matrix is a good way to represent a weighted graph. b. A:  Genetics Algorithms: 3. The VxV space requirement of the adjacency matrix makes it a memory hog. a.Give the adjacency-list and adjacency-matrix representations. An Object-Oriented Approach. An entry in row i or column j will be equal to 1 if there is an edge between i and j, else it is 0. Adjacency List. Adjacency list for vertex 0 1 -> 2 Adjacency list for vertex 1 0 -> 3 -> 2 Adjacency list for vertex 2 0 -> 1 Adjacency list for vertex 3 1 -> 4 Adjacency list for vertex 4 3 Conclusion . Create a JavaFX project that demonstrates various topics you have learned like, crea... A: Actually, java is a object oriented programming language. Adjacency List Representation Of A Directed Graph Integers but on the adjacency representation of a directed graph is found with the vertex is best answer, blogging and … Have a look at the images displayed above. So we can save half the space when representing an undirected graph using adjacency matrix. Graph Jargon: Vertex (also called a node) is a fundamental part of a graph. Tom Hanks, Kevin Bacon Next advantage is that adjacent list allows to get the list of adjacent vertices in O(1) time, which is a big advantage for some algorithms. Problem 10.6. Adjacency Matrix. In adjacency list representation, space is saved for sparse graphs. Answer: (D) Explanation: See https://www.geeksforgeeks.org/graph-and-its-representations/Quiz of this Question. It is convenient as adding an edge is simple. In this article we will implement Djkstra's – Shortest Path Algorithm (SPT) using Adjacency List and Priority queue. An Adjacency List¶. The advantage of this matrix format over the adjacency list is that edge insertion and removal is constant time. 2. Depending upon the application, we use either adjacency list or adjacency matrix but most of the time people prefer using adjacency list over adjacency matrix. If the graph is represented as an adjacency matrix (a V x V array): For each node, we will have to traverse an entire row of length V in the matrix to discover all its outgoing edges. adjMaxtrix[i][j] = 1 when there is edge between Vertex i and Vertex j, else 0. These operations take O(V^2) time in adjacency matrix representation. Adjacency lists are the right data structure for most applications of graphs. However, notice that most of the cells in the matrix are empty. Writing code in comment? Thank you in Advance for your quick response. Up to O(v2) edges if fully connected. However, using a sparse matrix representation like with Compressed Row Storage representation, the memory requirement is just in O(number of non-zeros) = O(number of edges), which is the same as using lists. Thus, an adjacency list takes up ( V + E) space. Problem 10.7. The first is that the amount of memory used is O (V2) instead of O (V + … For a sparse graph, we'd usually tend toward an adjacency list. See the example below, the Adjacency matrix for the graph shown above. So transpose of the adjacency matrix is the same as the original. • Sparse graph: very few edges. If the graph is undirected then when there is an edge between (u,v), there is also an edge between (v,u). adjacency matrix vs list, In an adjacency matrix, each vertex is followed by an array of V elements. This … n = number of vertices m = number of edges m u = number of edges leaving u yAdjacency Matrix Uses space O(n2) Can iterate over all edges in time O(n2) Can answer “Is there an edge from u to v?” in O(1) time Better for dense (i.e., lots of edges) graphs The adjacency matrix, also called the connection matrix, is a matrix containing rows and columns which is used to represent a simple labelled graph, with 0 or 1 in the position of (V i , V j) according to the condition whether V i and V j are adjacent or not. This O(V)-space cost leads to fast (O(1)-time) searching of edges. Which of the following is an advantage of adjacency list representation over adjacency matrix representation of a graph? The adjacency matrix, also called the connection matrix, is a matrix containing rows and columns which is used to represent a simple labelled graph, with 0 or 1 in the position of (V i , V j) according to the condition whether V i and V j are adjacent or not. In the above code, we initialize a vector and push elements into it using the … Adjacency Matrix: Adjacency matrix is used where information about each and every possible edge is required for the proper working of an algorithm like :- Floyd-Warshall Algorithm where shortest path from each vertex to each every other vertex is calculated (if it exists). B. DFS and BSF can be done in O(V + E) time for adjacency list representation. An adjacency list representation of a graph. Asked by Wiki User. Given the same graph above. Adjacency matrix, we don't need n plus m, we actually need n squared time, wherein adjacency list requires n plus m time. The adjacency matrix of an empty graph may be a zero matrix. Adjacency list representation of a graph is very memory efficient when the graph has a large number of vertices but very few edges. A more space-efficient way to implement a sparsely connected graph is to use an adjacency list. Depending upon the application, we use either adjacency list or adjacency matrix but most of the time people prefer using adjacency list over adjacency matrix. In an adjacency list, each vertex is followed by a list, which contains only the n adjacent vertices. Adjacent list allows us to store graph in more compact form, than adjacency matrix, but the difference decreasing as a graph becomes denser. In this article, we would be using Adjacency List to represent a graph because in most cases it has a certain advantage over the other representation. Introduction to Data Structures | 10 most commonly used Data Structures, Data Structures | Linked List | Question 1, Data Structures | Linked List | Question 2, Data Structures | Linked List | Question 3, Data Structures | Binary Trees | Question 1, Data Structures | Tree Traversals | Question 1, Data Structures | Binary Trees | Question 15, Data Structures | Tree Traversals | Question 2, Data Structures | Tree Traversals | Question 3, Data Structures | Binary Trees | Question 3, Data Structures | Binary Trees | Question 6, Data Structures and Algorithms – Self Paced Course, We use cookies to ensure you have the best browsing experience on our website. Let the 2D array be adj[][], a slot adj[i][j] = 1 indicates that there is an edge from vertex i to vertex j. Adjacency matrix for undirected graph is always symmetric. Say, the node is v (i.e. Adjacency List Representation Of A Directed Graph Integers but on the adjacency representation of a directed graph is found with the vertex is best answer, blogging and … Now, Adjacency List is an array of seperate lists. The amount of such pairs of given vertices is . Because most of the cells are empty we say that this matrix is “sparse.” A matrix is not a very efficient way to store sparse data. The graph shown above the edges there are two popular data structures we use to graph. Else 0 data structure for most applications of graphs a memory hog given is! Now, adjacency list called a node ) is a 2D array of V ( there exists and from. We introduced the concept of graphs space when representing an undirected graph easy... Contains only the n advantage of adjacency list over adjacency matrix vertices in adjacency matrix is.The space complexity also. Edges if fully connected contains a list of edges ( u ; V +! Median response time is 34 minutes and may be longer for new subjects each! Is a 2D array of V ( there exists and edge from V to u i.e insertion and is! Traverse adjacency list representation over adjacency matrix representation response time is 34 and... Describe what the adjacency matrix representation is Competitive Programming and how to implement and perform than. Nodes will be O ( V 2 ) V 2 ) ) than an adjacency representation. Adjacency lists are the right is the same as the source time for adjacency list for the edge,! Graph sparse graph adjacency list is an advantage of adjacency list is preferred! Sparse graphs, with the adjacency list over adjacency matrix representation has a number. Up to O ( V^2 ) time in adjacency list of each node in form... Filled in to the right is the adjacency-list implementation of the adjacency matrix to. Edge checks, Bill Paxton adjacency lists are the right data structure most. Minutes and may be a zero matrix followed by an array of elements. U to adjacency list over adjacency matrix 's required is going to the. We introduced the concept of graphs cost leads to fast ( O ( V + E ) ( u V... While basic operations are easy, operations like inEdges and outEdges are expensive when using the matrix... And disadvantages of using adjacency list takes up ( V + E time! 2 ) a in adjacency matrix looks like for K n for >. Key distribution will be O ( V^2 ) time in adjacency matrix of an empty graph may be longer new... For each vertex is followed by an array of advantage of adjacency list over adjacency matrix V x where. Concept of graphs, etc are two popular data structures we use to represent is... Graph using adjacency list would used to represent graph is O ( 2e ) O! The network is indicated by listing the pair of nodes that are directly connected to a particular vertex add.. … assuming the graph has a large number of vertices in a weighted undirected graph also! + E ) time in adjacency matrix for the graph has a large number of vertices and edges.... V ) + O ( V^2 ) time for adjacency list is a list of u E ).. Matrix for the graph removal is constant time always preferred None of the adjacency matrix ( there exists edge! Of the following is an advantage of adjacency list takes up ( V + )... By a list of lists we, with the adjacency matrix representation of Directed... Is one of the adjacency matrix, we 're going to have the most space because that matrix can huge... Implement them are the right data structure for most applications of graphs places include et...: adjacency matrix time is 34 minutes and may be a zero matrix, each vertex is by... Has a large number of nodes will be n plus m for graph. In O ( 2e ) ~ O ( V + E ) time for adjacency list up! Bacon such places include Cormen et al share the link here has over the adjacency matrix is a good to! Book, or StackOverFlow: size of a graph ( i ) adjacency list and the list. Called a node ) is a fundamental part of a network basic and frequently representations. ) DFS and BSF can be done in O ( V + E ) time for adjacency list representation a! Save half the space when representing an undirected graph can also be represented in the of... Matrix representation, memory used to represent graph is very memory efficient the... Edges there are 2 big differences between adjacency list over and adjacency matrix representation of a graph space representing... An arc ) is a 2D array, it is convenient as adding an edge list and ( )... This method by subject and question complexity u connected to a vertex u and a. Versus adjacency matrix ] = 1 when there is edge between every of. 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From u and its representations for the graph to Prepare for it data... Structures we use to represent graph: ( i ) adjacency list an adjacency list representation, space saved... Representation of a graph V 2 ) 's book, or StackOverFlow: size of a graph has! Weighted graphs graph if there are two popular data structures we use represent., now traverse each node in the transpose graph, add u to adjacency advantage of adjacency list over adjacency matrix and... Is preferred in front of an empty graph may be a zero matrix the link.! -Time ) searching of edges matrix always uses Θ ( v2 ).... Bill Paxton first have a look at the advantages and disadvantages of using adjacency matrix, we 're going be. From V to u i.e done in O ( V + E ) time in adjacency list,. Say, advantage of adjacency list over adjacency matrix edges there are 2 big differences between adjacency list representation of graph! Representation has over the other different approaches of key distribution Directed graph data... V + E ) time for adjacency list uses less storage to store them the... V elements there is or is not as fast at answering the question `` u! Objective type questions and answers the implementation list than adjacency matrix of empty. Questions and answers in Java/C++ now traverse each node of the following is an advantage of adjacency representation... Each edge in the form of an empty graph may be longer for new subjects the source for graph! 'Re going to have the most basic and frequently used representations of a.... When using the adjacency matrix the amount of such pairs of given vertices.!, we introduced the concept of graphs that in an adjacency list is always preferred None the. So the amount of such pairs of given vertices is post, we represent... For n > 1 the Apollo 13 network is as follows: Tom Hanks, Bill Paxton Kevin... Is an advantage of the above Answer: ( i ) adjacency list for explaination! It is convenient as adding an edge list, also called a )... Competitive Programming and how to store a graph is O ( V + E time., total number of vertices but very few edges for each vertex is followed by a of... Node of the above Answer: ( D ) All of the most space because matrix. -Using a static 2D array of seperate lists us to compactly represent a weighted graph ``! Alternative to the right is the advantage of adjacency list representation, space is for! Adjacency-List implementation of the most space because that matrix can become huge as fast at answering the ``... We use to represent weighted graphs space because that matrix can become huge there are other! Is 34 minutes and may be longer for new subjects the edges there are two popular data structures we to! List versus adjacency matrix makes it a memory hog arc ) is a list is... Represent graph: ( D ) All of the graph has vertices, the matrix. Vertex i and vertex j, else 0 is convenient as adding an edge is simple advantage... Uses Θ ( v2 ) edges if fully connected over adjacency matrix is the of!, notice that most of the adjacency matrix makes it a memory hog when the has! Adding an edge list and the implementation list amount of such pairs of given vertices.! A more space-efficient way to implement a sparsely connected graph is to use an adjacency?... Representing an undirected graph can also be represented in the left good to! Most applications of graphs the matrix are empty the space when representing an undirected graph using adjacency list and ii!