Consider the directed network G = (V,E) with N = 5 nodes and L = 8 links, in which node 1 points to nodes 2 and 3, node 2 points to node 4, node 3 points to nodes 2 and 4, node 4 points to node 2, and node 5 points to nodes 3 and 4. (d) Calculate the normalised in-degree centrality x; of each node of the network and rank the nodes, from the most to the least central, according to their in-degree centrality.

2. Consider a connected network of two individuals. At each period t, each individual forms beliefs as a weighted average of his own beliefs with weight p = [0, 1] and the other agent's beliefs with weight 1 - p. (d) If p = 0, what happens to beliefs of each player as t→∞? (e) Express b2, beliefs in period 2, as a function of initial beliefs bo and p. Comment on the relationship between p and the difference in beliefs. (f) (Harder) What value of p will cause beliefs to converge fastest? Relate this to the second eigenvalue of the updating matrix A (Hint: your answer to (e) is helpful here.)

Use powers of adjacency matrices to determine the number of paths of th e specified length between the given vertices length 4, v2 and v2

Compute the vertex set V and edge set E of the graph G = (V,E) whose Prufer Code is (3, 3, 3,3, 3, 3). Select one: OV={1,2,...,8} and E = {(1,3), (2, 4), (4, 3), (5, 3), (6, 3), (7, 3), (8, 7)} {(1,4), (2, 3), (4, 3), (5, 3), (6, 3), (7, 3), (8, 3)} %3D OV={1,2,..., 8} and E = OV= {1,2,... ,8} and E = {(1, 4), (2, 3), (4, 3), (5, 3), (6, 3), (7, 3), (8, 7)} OV= {1,2,..., 8} and E = {(1,3), (2, 3), (4, 3), (5, 3), (6, 3), (7, 3), (8, 3)} Clear my choice

Find the relation determined by the diagraph and give its matrix.

Determine the adjacency matrix of the given graph.

b.) Determine whether the graph is simple or not. If it is a simple the adjacency matrix of the graph and determine the no. of paths of length 2 that it has.

Consider the network below and calculate x, y and z

Draw the network defined by N = {1, 2, 3, 4, 5, 6} A = {(1,2), (1,3), (1,4), (1,5), (2,3), (2,4), (2,5), (3,4), (3,6), (4,5), (4,6)}

A graph with vertices X, Y, Z has the adjacency matrix. How many walks of length 3 are there from Y to Z?