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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
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?
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