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= 5 nodes and L ― Consider the directed network G = (V,E) with N : 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. (a) Draw the network and write down its adjacency matrix A. (b) How many weakly-connected components and how many non-trivial (i.e. with more than one node) strongly-connected components are there in the network? List all the nodes belonging to each one of these components. List all the nodes belonging, respectively, to the in-component and the out-component of each of the non-trivial strongly-connected components. շ 4, (c) Determine the in-degree sequence {kin, kin, kin, kin, kin) and the out-degree sequence {kout, kout, kout, kout, kout} of the network. Write down the average node in-degree, the average node out-degree, the node in-degree distribution Pin(k) and the node out-degree distribution Pout (k).

= 5 nodes and L ― Consider the directed network G = (V,E) with N : 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. (a) Draw the network and write down its adjacency matrix A. (b) How many weakly-connected components and how many non-trivial (i.e. with more than one node) strongly-connected components are there in the network? List all the nodes belonging to each one of these components. List all the nodes belonging, respectively, to the in-component and the out-component of each of the non-trivial strongly-connected components. շ 4, (c) Determine the in-degree sequence {kin, kin, kin, kin, kin) and the out-degree sequence {kout, kout, kout, kout, kout} of the network. Write down the average node in-degree, the average node out-degree, the node in-degree distribution Pin(k) and the node out-degree distribution Pout (k).

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.7: Applications
Problem 79EQ
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= 5 nodes and L ― Consider the directed network G = (V,E) with N : 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. (a) Draw the network and write down its adjacency matrix A. (b) How many weakly-connected components and how many non-trivial (i.e. with more than one node) strongly-connected components are there in the network? List all the nodes belonging to each one of these components. List all the nodes belonging, respectively, to the in-component and the out-component of each of the non-trivial strongly-connected components. շ 4, (c) Determine the in-degree sequence {kin, kin, kin, kin, kin) and the out-degree sequence {kout, kout, kout, kout, kout} of the network. Write down the average node in-degree, the average node out-degree, the node in-degree distribution Pin(k) and the node out-degree distribution Pout (k).
Transcribed Image Text:= 5 nodes and L ― Consider the directed network G = (V,E) with N : 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. (a) Draw the network and write down its adjacency matrix A. (b) How many weakly-connected components and how many non-trivial (i.e. with more than one node) strongly-connected components are there in the network? List all the nodes belonging to each one of these components. List all the nodes belonging, respectively, to the in-component and the out-component of each of the non-trivial strongly-connected components. շ 4, (c) Determine the in-degree sequence {kin, kin, kin, kin, kin) and the out-degree sequence {kout, kout, kout, kout, kout} of the network. Write down the average node in-degree, the average node out-degree, the node in-degree distribution Pin(k) and the node out-degree distribution Pout (k).
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