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I have a random thought connected to a network problem and I am curious if
anyone knows of literature in this area.  I would also welcome speculation
and discussion.

I have meta-network data.  The data is recorded in directed affiliation
networks, such that agents (people) are linked to resources.  In some cases
resources are linked to people.  In other cases resources are linked to
resources. (no discipline in the data entry unfortunately)  Therefore, I
have three networks: A=(agent x resource), B=(resource x agent), C=(resource
x resource).  I can construct a social network of people linked through
their common connection to a resource with the relational algebra:
AA'+B'B+AB.  AA' links people who both have directed links to a resource.
B'B links people who both have directed links from a resource.  AB links a
person linking to a resource with those connected from a resource.

This does not link people where an agent is connected to a resource; that
resource is connected to a second resource; and that resource is connected
to an agent.  I could do a relationship such as ACB, however that only will
connect agents with a path length of 3.  I would need to do ACCB to connect
agents with a path length of 4, ACCCB for path length 5 and so on.

Is it reasonable to assume that the strength of the link between agents
decays as the path length of connected resources increases.  For example
people linked to and from my academic department all know each other.
People linked to and from the Computer Science department all know each
other.  Both departments support the Network Science Center, therefore,
Behavior Science is linked to Network Science is linked to Computer Science
in network C above.  Most of the faculty in Behavior Science do not know
most of the faculty in Comptuer Science however, which would invalidate the
argument ACCB.

This kind of makes me think of "Sparsity of Effects" in statistically
designed experiments, where we are able to create more efficient
experimental designs by assuming that higher order interactions of model
terms are unlikely if main effects are insignificant.  This is not
universally true, but is effective for many applications.

What are your thoughts?  Is it a bad idea to assume a sparsity of effects in
chaining relationships together in relational algebra?



Ian McCulloh, Ph.D.
Major, U.S. Army
Assistant Professor
Network Science Center and
Department of Behavioral Sciences and Leadership
U.S. Military Academy
West Point, NY 10996

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