A directed graph is strongly connected if there is a path from u to v and from v to u for any u and v in the graph. A directed graph is weakly connected if the underlying undirected graph is connected Representing Graphs Theorem. In an undirected simple graph with N vertices, there are at most NN1 2 edges. Proof. By induction on the number of

In any Directed Graph, let's consider a node i as a starting point and another node j as ending point. For all (i,j) pairs in a graph, transitive closure matrix is formed by the reachability factor, i.E if j is reachable from i (means there is a path from i to j) then we can put the matrix element as 1 or else if there is no path, then we can

Consider the directed graph given below. Which one of the following is TRUE? (A) The graph does not have any topological ordering... PSRQ is the only topological ordering. Answer. Topological ordering of a directed graph is a linear ordering of its vertices such that for every directed edge "u->v" from vertex "u" to vertex "v", "u" comes Given a weighted, directed graph G = (V, E) with no negative-weight cycles, let m be the maximum over all pairs of vertices u, v V of the minimum number of edges in a shortest path from u to v. (Here, the shortest path is by weight, not the number of edges.) To determine whether a given graph is a multigraph, use the ismultigraph function. Creating Graphs. The primary ways to create a graph include using an adjacency matrix or an edge list. Adjacency Matrix. One way to represent the information in a graph is with a square adjacency matrix. The nonzero entries in an adjacency matrix indicate an edge

3. Consider the un-weighted directed graph G = (V, E) below. D b h g j k f (c) (5 points) Describe an algorithm that computes the component graph. Your algorithm must be as efficient as possible. (d) (5 points) Give the complexity of your algorithm.

Consider the directed graph shown below and answer the following questions: a. Is this system deadlocked? Yes the system is deadlocked as both P1 and P3 are both requesting R2 b. Which, if any, processes are blocked? P1 and P3. P1 must wait for R2, P3 must wait for R2 c. What is the resulting graph after reduction? Directed Acyclic Graph for the given expression is- Problem-03: Consider the following block and construct a DAG for it- (1) a = b x c (2) d = b (3) e = d x c (4) b = e (5) f = b + c (6) g = f + d . Solution- Directed Acyclic Graph for the given block is- Problem-04: Optimize the block in the Problem-03. Solution- Step-01 Consider the algorithm below whose input is a directed graph G with nodes 1..N and with a edges. It computes (into T[i]) for each i ∈ 1..N the number of edges that have i as target. The algorithm interacts with G only through the interface operator allFrom. Few more details to answer this question : Matrix representation is given as

We introduce a new measure of complexity (called spectral complexity ) for directed graphs. We start with splitting of the directed graph into its recurrent and nonrecurrent parts. We define the spectral complexity metric in terms of the spectrum of the recurrence matrix (associated with the reccurent part of the graph) and the Wasserstein distance.

1 Answer to Assignment 12 on Chapter 29 1. Consider the directed graph that appears in the Figure below: a. In what order will a breadth-first traversal visit the vertices when you begin at vertex A ? B. Repeat Part a , but perform a depth-first traversal instead. Given a Directed graph of N vertices and M edges, the task is to find the minimum number of edges required to make the given graph Strongly Connected.. Examples: Input: N = 3, M = 3, source[] = {1, 2, 1}, destination[] = {2, 3, 3} Output: 1 Explanation: Adding a directed edge joining the pair of vertices {3, 1} makes the graph strongly connected. Hence, the minimum number of edges required is 1.

Lecture #2: Directed Graphs - Transition Matrices. A graph is an object that consists of a non-empty set of vertices and another set of edges.When working with real-world examples of graphs, we sometimes refer to them as networks.The vertices are often called nodes or points, while edges are referred to as links or lines.The set of edges may be empty, in which case the graph is just a For a Directed graph , there are 2 defined degrees , 1. Indegree 2. Outdegree For a directed graph G=(V(G),E(G)) and a vertex x1∈V(G), the Out-Degree of x1 refers to the number of arcs incident from x1. That is, the number of arcs directed away fr... 7. Award: 2.50 out of 2.50 points 8. Award: 2.50 out of 2.50 points Score: 133.33/140 Points 95.24 % Consider the given directed multigraph. References Section Break Chapter: 10 Graphs Section: 10.02 Graph Terminology and Special Types of Graphs a) What is the number of vertices for the given graph? 4 Identify the points that connects the edges/lines of the given graph. 1.For the directed graph below, nd the strongly connected components and draw the DAG of strongly connected components. A C J B D F E G H A BE CDFH G 2.Execute DFS on the following undirected graph starting at node D breaking ties alphabetically. Mark the pre and post values of the nodes. A C J B D F E G H Node pre post A 3 16 B 2 17 C 4 15 D 1 An adjacency list is a two-column matrix that abstractly represents the edge relations of a graph without needing to physically draw the graph. Each row of the adjacency list encodes an edge {u, v} by placing u in the first column and v in the second column (or vice-versa).. For example, consider the following graph: The adjacency list of this graph is given below (the rows could be given in

The objects are called as graph nodes or vertices and the edges symbolize paths between different graph nodes. A graph can be a directed or undirected graph. A directed graph is the one in which the edges E (x,y) have orientation or direction i.E they consist of … 4.2 Directed Graphs. Digraphs. A directed graph (or digraph) is a set of vertices and a collection of directed edges that each connects an ordered pair of vertices. We say that a directed edge points from the first vertex in the pair and points to the second vertex in the pair. We use the names 0 through V-1 for the vertices in a V-vertex graph. Glossary. Question: Measurements based on geodesic distance consider graph G in given figure below and calculate the following terms. I. Eccentricity . Ii. In case of directed graph, the number of permutation would be 3 (as order of nodes becomes relevant). Hence in this case the total number of triangles will be obtained by dividing total count by 3. For example consider the directed graph given below . Following is the implementation.

But most work in graph theory concentrates instead on undirected graphs.. Because graph theory has been studied for many …

If a starting point (eg: vertex 0) and a maximum depth allowed is specified (eg: 5), what algorithm can be used to find all possible paths (note: a... Algorithm data-structures graph directed-graph Output: Given directed graph is eulerian . Time complexity of the above implementation is O(V + E) as Kosaraju’s algorithm takes O(V + E) time. After running Kosaraju’s algorithm we traverse all vertices and compare in degree with out degree which takes …

P is true for undirected graph as adding an edge always increases degree of two vertices by 1. Q is true: If we consider sum of degrees and subtract all even degrees, we get an even number because every edge increases the sum of degrees by 2. So total number of odd degree vertices must be even. Directed: A directed graph is a graph in which all the edges are uni-directional i.E. The edges point in a single direction. Weighted: In a weighted graph, each edge is assigned a weight or cost. Consider a graph of 4 nodes as in the diagram below. As you can see each edge has a weight/cost assigned to it. Solution for 3. Consider the graph of the function y = f(x) given below: 5 4. -3 2 1- -5 -4 -3 -2 -1 1 2 3 4 6 -1 -2 -3 -4 (a) Consider the transformation 2f(-x…

The graph cannot be reduced because P3 is waiting on R3 which receives its information from R1 in the chain. 3. For the systems described in Questions 13 through 16 below, given that all of the devices are of the same type, and using the definitions presented in the discussion of the Banker’s Algorithm, answer these questions: a. 3) Consider the directed acyclic graph shown in the figure below. Determine whether each of the fol- lowing independence or conditional independence assumptions are valid according to the constraints given by the graph To receive full credit, make sure you show your steps clearly (to … Cons of adjacency matrix. The VxV space requirement of the adjacency matrix makes it a memory hog. 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.. While basic operations are easy, operations like inEdges and outEdges are expensive when using the adjacency matrix representation. Consider a weighted directed graph G=(V,E) in which each edge has an integral weight between 1 and 6. The graph is given as a list of triplets of the form (v,u,w). The triplet (v,u,w) corresponds to a single edge from the vertex v to the vertex u, whose weight is w. The goal is to sort the vertices according to the total sum of outgoing-edges In graph theory, a tree is a special case of graphs. In this tutorial, we’ll explain how to check if a given graph forms a tree. We’ll explain the concept of trees, and what it means for a graph to form a tree. Also, we’ll discuss both directed and undirected graphs. Finally, we’ll present a simple comparison between the steps in both Given a graph (can be directed or undirected), with vertices and edges , a walk of the graph is a sequence of alternating vertices and edges such that ... Consider, again, the graph below: Examples of paths include: (it is a path of length 3) (it is a path of length 1) Consider the following directed graph: The number of different topological orderings of the vertices of the graph is... GATE CSE 2016 Set 1... Consider the following sequence of nodes for the undirected graph given below. 1.A b e f d g c 2.A b e f c g d 3.A d... GATE CSE 2008. Several characterizations of singularity for mixed graphs were provided in [1]. It is natural to ask for similar characterization of singularity for the weighted directed graphs. In this section, we provide some characterizations of the singular weighted directed graphs. Example 2. Consider the weighted directed graph G shown below. Given a directed graph with weights on the edges, and is asked to ﬁnd a subset of edges with minimum total weight that intersects every cycle in the graph. W e assume that all The best directed graph is the graph that encodes only one of the CI relationships (see the mid-left gure below) that stands for fB??DjA[Cg. D)There are also directed graphs whose independence relationships cannot be captured by undirected models. Any directed graph with converging connection makes an example, see the graph on the right in the Representation of an undirected and directed graph is given below: Adjacency matrix representation of a weighted graph. For weighted graph, the matrix adj[ ][ ] is represented as: If there is an edge between vertices i and j then adj[i][j] = weight of the edge (i, j) otherwise adj[i][j] = 0. Given a graph with both directed and undirected edges. It is given that the directed edges don’t form cycle. How to assign directions to undirected edges so that the graph (with all directed edges) remains acyclic even after the assignment? For example, in the below graph…

Given the graph below, use Dijkstra’s algorithm to find the shortest path (More details included) Ask Question Asked 5 years, 5 months ago... Dijkstra's Algorithm on a Directed Graph with Negative Edges Only Leaving the Source. 2. Dijkstra's Shortest-Path Algorithm. 2.

Degree of Vertex in an Undirected Graph. An undirected graph has no directed edges. Consider the following examples. Example 1. Take a look at the following graph − In the above Undirected Graph, deg(a) = 2, as there are 2 edges meeting at vertex 'a'. Deg(b) = 3, as there are 3 edges meeting at vertex 'b'. Question: Consider The Directed Acyclic Graph Below. How Many Topological Orderings Does It Have? (clue, Check The First Exercise Solved In The Section Of Solved Exercise Of Chapter 3 Reference Book) 04 02 03 08 Question 5 15 Pts An Algorithm To Find All The Connected Components Graph Could Be: Start Given Nodes And Run BFS, Check If There Is A Node In The Graph The following are some of the variants of the graph. #1) Directed Graph. A directed graph or digraph is a graph data structure in which the edges have a specific direction. They originate from one vertex and culminate into another vertex. The following diagram shows the example of directed graph. You are given a directed graph and two vertices on it. Your task is to find if there exists a path between the first vertex to the second vertex or not... Consider the following graph: Input to construct the above graph:... In the Graph G in the image below, we find whether there exists a path between node 1 and node 6 using BFS. To find if Solution for 1.) Consider the graph of y = f(x) given below. 3. --2 4 -2 (i) State the value of the given quantity, if it exists. If it does not exist, explain… Introduction Graphs are a convenient way to store certain types of data. The concept was ported from mathematics and appropriated for the needs of computer science. Due to the fact that many things can be represented as graphs, graph traversal has become a common task, especially used in data science and machine learning. Graph traversal refers to the process of visiting nodes (aka vertices

V2V. A directed graph is simple if it has no loops (that is, edges of the form u!U) and no multiple edges.

A-> B,C A-> A,D,E,F C->AF Assume that the PageRank values for any page m at iteration 0 is PR(m)=1 and teleportation factor for iterations is $\beta$=0.85.Perform the page rank algorithm and determine the rank for every page at iteration 2. Consider the directed graph shown in the figure below. There are multiple shortest paths between vertices S and T. Which one will be reported by Dijstra?S shortest path algorithm? Assume that, in any iteration, the shortest path to a vertex v is updated only when a … Calculus Q&A Library Problem 1 Consider the function f whose graph is given below: 2 y 3 2. -2 1. State the domain and range of f. 2. Find all the values on the closed interval [-3, 3] for which ƒ is discontinuous. For each value, state at least one reason why the function fails to be continuous there. We consider directed graph algorithms in a streaming setting, focusing on problems concerning orderings of the vertices. This includes such fundamental problems as topological sorting and acyclicity testing. We also study the related problems of nding a minimum feedback arc set (edges whose removal yields an acyclic graph), and nding a sink vertex. 1. Datasets of Normal Crawl. We consider all the YouTube videos to form a directed graph, where each video is a node in the graph. If a video b is in the related video list (first 20 only) of a video a, then there is a directed edge from a to b.Our crawler uses a breadth-first search to find videos in the graph. That is, both u and v are reachable from each other. In other words, two vertices of directed graph are in the same component if and only if they are reachable Given the multiple uses of the word “graph”, I should perhaps have emphasized in the post that by a directed graph, I mean one in which there can be multiple edges. Formally, by a directed graph I mean a set V V, a set E E, and two functions s, t: E → V s, t: E \to V (assigning to an edge its source, or tail, and its target, or head).

Consider the graph given below. Determine which sequences of transformations could be applied to the parent function, f(x) = x, to obtain the graph above. Reflect over the x-axis, vertically stretch by a factor of 2, and then shift up 6 units Shift left 2 units, reflect over the y-axis, and then vertically stretch by a factor of 6 Shift left 3

Consider the directed resource graph given below. (R1-2 means Resource 1 has 2 units of non-sharable resource.) a. Is this system, as a whole, deadlocked? B. Are there any deadlocked processes? C. Three processes are requesting resources from R2. I. Which requests would you satisfy to minimize the number of processes involved in the deadlock? Ii. A bridge in a graph is an edge that, if removed, would separate a connected graph into two disjoint subgraphs. A graph that has no bridges is said to be two-edge connected. Develop a DFS-based data type Bridge.Java for determining whether a given graph is edge connected. Web Exercises. Find some interesting graphs. Are they directed or undirected? Find CycleA graph is a type of data structure that consists of nodes and edges that connect the nodes. An edge has a start node and end node, and we will only consider directed edges.The figure_consider the graph with 8nodes A directed graph. Vertices = cities, intersections, landmarks, etc. A pair of directed edges between each pair of connected nodes, each edge giving the travel time in one of the two directions. (b) Chess board – an 8 x 8 board used for a game of chess. Each square on the board is either empty or contains a chess piece.

Consider the following sequence of nodes for the undirected graph given below I. A b e f d g c II. A b e f c g d III. A d g e b c f IV. A d b c g e f A depth first search is started at node a. The nodes are listed in the order they are first visited. Which all of the above is possible output? (GATE: 2008) 3. Consider an infinite directed acyclic graph (DAG) with a unique source vertex X. Let the collection of vertices at distance k from X be called the kth layer, and suppose every non-source vertex has indegree d ≥ 2. At layer 0, the source vertex is given a random bit.