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HW 1 solns

# HW 1 solns - Networks Spring 2008 David Easley and Jon...

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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) Let’s 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.

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HW 1 solns - Networks Spring 2008 David Easley and Jon...

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