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I wonder (and would not be surprised) if the nodes are always defined by phone number alone. Meaning, if you made a restaurant reservation at the italian place by your house, you're two hops from everyone who's ever called or been called by them.


From what I've seen while studying in an academic research lab:

The tools student researchers were designing (commonly in Jython at my school, btw) integrated multiple networks at once with surprising fluency. It was often a dopamine-stimulating part of demos to say something such as, "See, this is the extent of the phone number graph, and now we add the email data <click> and now we add facebook data <click> and now resumes <click> and now mailing lists <click> and shopping records!"

Also, they use discrimination functions to weed out nodes with heavy use, like a restaurant take out number. Typically, they can histogram # of connections and use central moments such as kurtosis to determine if a particular node has too many connections.


It's probably a directed graph, and the hops are directed paths.


That seems unlikely; otherwise you could stay off the radar by just establishing a protocol of only calling your terrorist friends, rather than having them call you (or vice versa, if that's the direction a "hop" indicates).


The scenario you describe wouldn't be helped by using an undirected graph, since common hubs (technical support, sex chat lines, sales cold calls, etc.) would connect almost everything with very short path lengths. A common compromise is to throw away all non-reciprocated edges and then use an undirected graph. Your protocol would still keep you off the radar, which illustrates some of the difficulties of the approach.


Why would direction make a good filter?


It's not a filter, but you're losing a lot of information by discarding direction. Without direction, most nodes will likely be part of a giant connected component with small diameter, due to the presence of hubs. See my other comment in this thread.




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