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BL40A2010 Introduction to IoT-Based Systems

Assignment 3, 09.02.2022

Author: David Vigh

(1) Compute the following for a ring topology of N>=3 nodes, considering that the network in unweighted and the links are directed. The result will give these number as a function of N.

Answer: In ring topology, each node is connected to 2 other nodes. All nodes have the same characterization.

(a) Degree of nodes: 2, regardless of N

(b) Adjacent matrix: A=

(0 1 0 0 ... 1)

(1 0 1 0 ... 0)

(... ... ... ... ... ...)

(1 0 0 0 ... 0)

(d) Clustering coefficient of the nodes:

1, when N=3 as the neighbors form complete graphs

0, when N>3

(2) Use Network X to draw and analyze a ring topology with 5 nodes. Verify if the results previously obtained are valid.

import networkx as nx import matplotlib.pyplot as plt import scipy as sp import numpy as np G = nx.Graph() G.add_nodes_from([0, 4]) G.add_edges_from([(0, 1), (1, 2), (2, 3), (3, 4), (4, 0)]) nx.draw_networkx(G, node_color='black', font_color='white', edge_color='black', font_weight='bold', node_size=700) plt.axis('off') plt.show()

A = nx.adjacency_matrix(G,nodelist=sorted(G.nodes())) print(A.todense())

G.degree()

nx.clustering(G)

nx.diameter(G)

(3) Analyze the ring topology with size 20 (N=20) as a communication network (i.e. how data travel to a point to another in the network) based on the node degree, the network diameter and the cluster coefficient.

Answer: From question 1, nodes in a ring network topology are connected in a ring or a loop. Therefore, when data is sent, it needs to go around the ring, passing from one computer system to the next until it reaches its goal. With this large size (N=20), the possibility of one node failing increases significantly, if that happens, data can't be transmitted as the ring was broken. However, network collisions are avoided as data is transferred in one direction. Since the network is not cauterized, it is highly exposed against attacks involving nodes and links.

(4) Consider the ring network from the previous question. The network performance depends on its diameter. As a designer, you can add one new node in the network (and an unlimited number of links that this node is part). Justify your decision and evaluate how much better the network is. Generalize this finding as a function of N.

Hint: Follow Exercise 1 approach to generalize the finding.

Answer: In this case, the best decision would be to add the new node to the center of the ring topology, and connect it to every other node. It makes the network more robust as it provides another path, if one node fails. With this new network, the diameter will always be 2 and the clustering coefficient of the outer nodes will increase from 0 to 0.6666. Center node has N degree of nodes, and outer nodes will have 3.