Consider the directed network G = (V,E) with N = 5 nodes and L = 8 links, in whichnode 1 points to nodes 2 and 3, node 2 points to node 4, node 3 points to nodes 2 and4, node 4 points to node 2, and node 5 points to nodes 3 and 4.(g) Calculate the N x N matrix d whose element dij is the length of the shortestpaths from node i to node j. Calculate the efficiency centrality r; of each node ofthe network and rank the nodes, from the most to the least central, according totheir efficiency centrality.

Let's start with calculating the shortest path lengths between nodes: 1. Constructing the adjacency…

Answered: Consider the directed network G = (V,E)…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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In a two-industry economy. it is know that industry I uses 10 cents of its oWn product and 60 cents of commodity II to produce a dollar's worth of commodity I: industry II uses none of its own product but uses 50 cents of commodity I in producing a dollar's worth of commodity II: and the open sector demands RM1000 billion of commodity I and RM2000 billion of commodity II. a) Write out the input matrix. the Leontief matnx. and the specitic input-outpuf matrix equation for this economy. b) Find the solution output levels by Cramer's nile. 2. Delete, in rotate pa
For the complete Ely) = Bo + B1X1+ B2x2+ B3X3+ BaX1X2+ B5X1X3, which model %3D of the following is not a possible reduced model? E(y) = Bo + B1X1 Ely) = Bo + B1X1 + B2x2+ B3X3 Ely) = Bo + B1x+ B2x2 Ely) = Bo + B1X1+ B2X2+ B3X1X2
Consider the adjacency matrix 0 0 1 1 1 0 0 0 0 1 0 1 1 0 0 1 1 0 of a graph with nodes labeled a,b,c,d,e and f and lexiographically ordered rows and columns. 1 1 1 0 1 1 1 0 1 1 0 0 0 1 0 1 0 0. Suppose the above adjacency matrix identifies the network in a small company, where nodes represent workers and edges indicate that those workers interact during the week. The company has a single team leader and two different projects, one larger than the other. Workers in the same project interact often during the week. a) State which node represents the team leader, justifying your answer. b) State whether all workers are involved in at least one project and whether there is any worker, apart from the team leader, who works simultaneously on both projects. c) Explain what happens to the graph if the team leader suddenly resigns. Your response should be written in sentences.
Train the auto associative network for input vector [1 -1 -1 1] and also test the network for the same input vector. Test the auto associative network with one missing, and two missing entries in test vector.
Let A be any coefficient matrix of size m×n (m rows, n columns).Part A) For the linear system Ax = b, how many equations are there? How many unknowns are there? Part B) Suppose m = 4 and n = 2. The linear system is called overdetermined because there are more equations than unknowns. For each of the following statements, write an example of A to make the statement true, or state that no such example exists.i. For any b, Ax = b has at least one solution. (existence)ii. For any b, Ax = b has at most one solution. (uniqueness)iii. For any b, Ax = b has exactly one solution. (existence and uniqueness) Part C) Suppose m = 2 and n = 4. The linear system is called underdetermined because there are more unknowns than equations. For statements i-iii in (Part B), write an example of A to make the statement true, or state that no such example exists. Part D) Suppose m = 4 and n = 4. The linear system now has a square coefficient matrix. For statements i-iii in (b), write an example of A to make…
Now consider the network (G, w) such that V(G) = {V₁, V2, U3, U4, V5, V6, U7}, E(G) = {V1V2, V1V3, V2V3, V2V4, V2V5, V3V5, V3V6, V4V5, V5V6} and w(v₁v₂) = 1, w(v₂v₁) = 2, w(v3v6) = 1, w (v₁v3) = 4, w(v₂v5) = 3, w(v4v5) = 1, w(v₂V3) = 4 w(v3v5) = 4 w(v5v6) = 3. the spanning three of (GW) is V₂ V6 V5 J 1 2 V4 Show that the spanning tree unique minimum spanning tree of the network (G, w). V/₂ is the
Find an optimal parenthesisation of a matrix chain product whose sequence of dimensions is(4, 8, 7, 2, 3).
Consider the network with N = 4 nodes and adjacency matrix A given by 0 1 1 1 0 1 1 A = 0000 0000 (a) Calculate the number of links in the network and draw the network. Is the network directed or undirected? (b) Is the network weakly connected? Is the network strongly connected? List the nodes belonging to each of the strongly-connected components in the network.
Let A be a matrix and mathbfb be a matrix and a vector defined by 1 2 1 -1 1 b = 1 1 3 Compute x* that minimizes ||Ax - b|.
Solve the following system using the Gaussian algorithm: 2x1 - x2 + 3x3 = 0 -2x1 + x2 - X3 = -2 x1 - 3x2 + 6x3 = 3 Let x be the vector x = |x2, where x1, x2 and x3 are solutions of the system, and y be the vector y =|1 Evaluate the scalar product of x and y. [Please enter your answer numerically in decimal format. You will be marked correct as long as what you enter is within 0.25 of the correct answer. So for example, if the correct answer is 6.78 then any input that lies between between 6.53 and 7.03 will be marked as correct.] Answer:
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