Consider the decision model/game theoretic model from Chapter 19 for the spread of a new behavior through a social network. Suppose we have the social network depicted in Figure 2; suppose that each node starts with the behavior B, and each node has a threshold of q = 2/5 for switching to behavior A.Now, let c and d form a two-node set S of initial adopters of behavior A. If other nodes follow the threshold rule for choosing behaviors, which nodes will eventually switch to A? Give a brief (1-2 sentence) explanation for your answer.Find a cluster of density greater than 1 − q = 3/5 in the part of the graph outside S that blocks behavior A from spreading to all nodes, starting from S, at threshold q. Give a brief (1-2 sentence) explanation for your answer.Suppose you were allowed to add a single edge to the given network, connecting one of nodes c or d to any one node that it is not currently connected to. Could you do this in such a way that now behavior A, starting from S and spreading with a threshold of 2/5, would reach all nodes? Give a brief explanation for your answer. kFigure 2: Starting from nodes c and d, the new behavior A fails to spread to the entiregraph.

Given: The node starts from behavior - B Each node threshold behavior (A)9 = 2/5

Answered: Consider the decision model/game…

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

Related questions

Question

Consider the decision model/game theoretic model from Chapter 19 for the spread of a new behavior through a social network. Suppose we have the social network depicted in Figure 2; suppose that each node starts with the behavior B, and each node has a threshold of q = 2/5 for switching to behavior A.
1. Now, let c and d form a two-node set S of initial adopters of behavior A. If other nodes follow the threshold rule for choosing behaviors, which nodes will eventually switch to A? Give a brief (1-2 sentence) explanation for your answer.
2. Find a cluster of density greater than 1 − q = 3/5 in the part of the graph outside S that blocks behavior A from spreading to all nodes, starting from S, at threshold q. Give a brief (1-2 sentence) explanation for your answer.
3. Suppose you were allowed to add a single edge to the given network, connecting one of nodes c or d to any one node that it is not currently connected to. Could you do this in such a way that now behavior A, starting from S and spreading with a threshold of 2/5, would reach all nodes? Give a brief explanation for your answer.