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.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 EASLEY/KLEINBERG
 Sociology, Interpersonal ties, strong triadic closure, David Easley

Click to edit the document details