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Eric, one could also use a dyadic modification of the Newman-Girvan
shortest path betweenness (as in resistor networks).

--Moses

On Tue, Jun 7, 2011 at 10:09 PM, Eric Lin <[log in to unmask]> wrote:
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>
> Hi,
>
> I'm looking for a network measure that I imagine may exist already, but I
> haven't been able to find it.  I'm thinking about a measure of contagion.
> This blends the concepts of distance and redundancy.
>
> Geodesic distance takes the shortest distance between two nodes, and
> redundancy focuses on eliminating the double counting if there are multiple
> paths to the same node.  However, geodesic distance ignores the other paths
> that are not the shortest.  And redundancy seems to focus on removing
> redundant paths rather than emphasizing them as alternate opportunities to
> transmit.
>
> I'm looking for something that will take a weighted sum of all the possible
> paths from one node to another.
>
> For example.  For a given person A, he is directly connected to B through an
> edge that signifies a meeting taking place.  Imagine they have several
> meetings, so there are multiple direct connections between the two (say 5).
>  In addition, A meets with C 4 times and B meets with C 3 times.  A and B
> have a second degree connection through C a total of 3 times.
>
> If we wanted to measure how many opportunities A has transmit something to
> B, we could add up the edges in the following weighted way:
>
> direction connection:  weight_1 * 5 (meetings)
> indirect connection : weight _2 * 3
>
> and add this up, where the weight_1 is a heavier weight than weight_2.
>
> Does a measure like this exist?  If so, what is it called are there examples
> of this measure being used?
>
> Thanks!!
>
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