This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Networks: Spring 2008 Solution Set 1 David Easley and Jon Kleinberg (1) Node A has two ties: a strong tie to node B and a strong tie to node C . In order for node A to satisfy Strong Triadic Closure there must also be a tie (at least a weak one) between nodes B and C . In fact, there is a strong tie between nodes B and C . So we conclude that node A does satisfy the Strong Triadic Closure property. Node B has strong ties to node A and node C , and a weak tie to node D . We have already observed that there is also a strong tie between A and C . Also, since the tie to D is weak, Strong Triadic Closure does not have any implications here. Therefore, B also satisfies the Strong Triadic Closure property. Node C has strong ties to A , B and E . Again, we have already observed that there is a strong tie between A and B . However, Strong Triadic Closure would imply that there should also be ties between A and E , and between B and E . Since there is not a tie between A and E , node C does not satisfy the Strong Triadic Closure Property. Even if we added a weak tie connecting A to E in the network, node C would still not satisfy the Strong Triadic Closure property because there is also no tie connecting B to E . Since D and E both have at most one strong tie, Strong Triadic Closure has no impli cations for them. We therefore conclude that they both satisfy the Strong Triadic Closure property. Strong Triadic Closure says that if a node has two strong ties, there should also be a tie (at least a weak one) between those two nodes. Node E , for example, has no strong ties so it satisfies this condition. (2) Lets just start by connecting nodes and see how far we get. First we connect nodes A and D . This completes one triangle between A , B and D . Since the edge between A and B is positive and the edge between B and D is negative, the edge between A and D must be negative to preserve structural balance....
View
Full
Document
This homework help was uploaded on 04/22/2008 for the course INFO 2040 taught by Professor Easley/kleinberg during the Spring '08 term at Cornell University (Engineering School).
 Spring '08
 EASLEY/KLEINBERG

Click to edit the document details