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Re: Empirical Studies - Awareness of friends' friends

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Thu, 28 May 2015 14:42:19 +0300

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 ```***** To join INSNA, visit http://www.insna.org ***** Hi Ian, What one can say from a graph-theoretic point of view is that what you're asking depends on how densely and closely (parsimoniously) egos are knitted to each other. In other words, this is a question of how tidily multiple egos are extracted from the whole network. To give a couple of examples let me denote by SE the set of egos and by FF the set of friend's friends of all egos such that any actor in FF is not an ego. (|SE| denoted the the total number of egos and |FF| the total number of friend's friends: notice that, in general, FF is a multi-set.) A trivial case is when every actor in the network is an ego, in which case |FF| is empty. Further, there is the following interesting definition in graph theory: A set S of actors is called "dominating set of actors" if any actor is either in S or adjacent to an actor in S. Furthermore, a set S of actors is called a "minimum dominating set" (MDS) if the cardinality of S is minimum among the cardinalities of any other dominating set. In addition, the cardinality of a minimum dominating set is called "domination number" of the network. These notions are quite useful because they allow us to answer the following question: How should egos be selected from a network in such a way that (1) every actor that is not selected as an ego may be adjacent to an ego (i.e., it may be an alter of some ego) and (2) the number of so selected egos becomes minimal? Apparently, the answer to this question (from the point of view of graph domination theory) is to select egos in such a way that SE becomes a MDS, i.e., so that |SE| might become equal to the domination number of the network. Let me call "set of dominating egos" (SDE) this selection of egos. Obviously an upper bound of |SDE| is n/2, where n is the total number of actors in the network. However, it is not hard to show that a lower bound of |SDE| is (diam + 1)/3, where diam is the network diameter. --Moses On Thu, May 28, 2015 at 6:24 AM, Ian McCulloh <[log in to unmask]> wrote: > ***** To join INSNA, visit http://www.insna.org ***** > Hello! > > Is anyone aware of any empirical social network studies that evaluate an > ego's accuracy in reporting (or being aware of) his friends' friends (2nd > order connections)? Even better would be extending this to 3rd, 4th, 5th, > etc order. > > I'm familiar with the literature on social network search, such as > Granovetter's famous six degrees experiment and Duncan Watts' more recent > email version, but this is not really what I'm looking for. > > I want to know how aware is an individual of network connections that exist > beyond their immediate ties. > > The closest literature I have found is David Krackhardt's cognitive social > structure work, however, the networks are small networks and I would prefer > to see data where a larger diameter is possible. > > I appreciate any leads you might have. > > Kind Regards, > > Ian > > Ian McCulloh, Ph.D. > Johns Hopkins University > _____________________________________________________________________ SOCNET > is a service of INSNA, the professional association for social network > researchers (http://www.insna.org). To unsubscribe, send an email message to > [log in to unmask] containing the line UNSUBSCRIBE SOCNET in the body of > the message. _____________________________________________________________________ SOCNET is a service of INSNA, the professional association for social network researchers (http://www.insna.org). To unsubscribe, send an email message to [log in to unmask] containing the line UNSUBSCRIBE SOCNET in the body of the message.```