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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
Network Science Center and
Department of Behavioral Sciences and Leadership
U.S. Military Academy
West Point, NY 10996
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