***** To join INSNA, visit http://www.insna.org ***** On Mon, 16 Jan 2006, Joshua O'Madadhain wrote: [...] > I'm not sure this formulation is correct, for three reasons: > (1) I don't see why it should matter whether any two 1s are in > adjacent rows/columns, since the ordering of the vertices is > presumably arbitrary. > (2) I don't see how these conditions guarantee that the diameter is > <= 2. (One easy way to do this is to square the adjacency matrix A, > and check to make sure that A_ij + (A^2)_ij > 0 for all i, j such > that i != j.) > (3) How do these conditions guarantee that the resultant graph is > minimal? Ooops.. my mistake: Writing this I was thinking of his example where n = 6 and degree = 3. Thus, I've constructed a third sociomatrix as a case other than the two he has given. However, I agree with you, in general the situation is much more complicated. --Moses > I'd be happy to find that it's simply the case that my graph theory > is rusty, of course... > > A final question for Juno: what is the difference metric that you're > using? > > Good luck-- > > Joshua O'Madadhain > > > > > Incidentally in your example (n = 6) there is a third graph that > > you need > > to consider and this is the following > > > > n 1 2 3 4 5 6 > > 1 1 1 1 > > 2 1 1 1 > > 3 1 1 1 > > 4 1 1 1 > > 5 1 1 1 > > 6 1 1 1 > > > > --Moses > > > > > > On Mon, 16 Jan 2006, Juno Blaauw wrote: > > > >> ***** To join INSNA, visit http://www.insna.org ***** > >> > >> Hello SOCNETTERS, > >> > >> My name is Juno Blaauw and I am a political research student at the > >> University of Amsterdam. I am writing this e-mail on behalf of > >> Meindert > >> Fennema, Jean Tillie and myself. > >> > >> Meindert Fennema and Jean Tillie are studying ethnic civic > >> communities. > >> Lately they have been interested (among other things) in > >> introducing a > >> normative definition of a civic community and in measuring the > >> difference > >> between a given empirical civic community and this normative > >> definition. I > >> have been working with them on this (thesis). We have been able to > >> formulate > >> a, in our eyes, satisfactory definition of a normative civic > >> community, > >> which we have called an 'old boys civic community', and a measure > >> for the > >> above mentioned difference. The only problem is that our normative > >> definition does not lead to one unique social network. In other > >> words: on a > >> given number of nodes many social networks qualify as old boys civic > >> communities. > >> > >> Before getting to the specific question we would like to ask you all, > >> I willfirst give you our definitions. First of all our definition > >> of a > >> civic > >> community: "a civic community [...] consists of many voluntary > >> associations > >> that are related to each other by way of overlapping membership and > >> interlocking directorates' (Fennema, 2004, p. 433.)" The voluntary > >> associations are formal organisations and the interlocking > >> directorates are > >> people that are board members of two of these organisations. Thus, > >> a civic > >> community can be defined as the set of formal organisations and > >> the ties, in > >> the form of interlocking directorates, between them. A civic > >> community that is > >> defined like this can be depicted as a graph were the nodes > >> representorganisations and the lines interlocking directorates. > >> > >> Secondly, our definition of an old boys civic community: A civic > >> community > >> is an old boys civic community if and only if (a) any two > >> organisations are > >> either directly linked by an interlocking directorate or have a > >> maximum of > >> two interlocking directorates between them and (b) each of the > >> civiccommunity's organisations is adjacent to the same number of > >> otherorganisations. > >> > >> Now, the question we would like to ask all of you is this: how can > >> we find > >> out how many and which old boys civic communities there are on a > >> givennumber of nodes? Note that we are only interested in minimal old > >> boys civic > >> communities, that is in old boys civic communities with a minimal > >> number of > >> interlocking directorates (ties). > >> > >> To illustrate our problem: Here are two minimal old boys civic > >> communities > >> on six nodes. Are these the only two? If so, how can we proof > >> that? If not, > >> how can we find the other ones? > >> > >> n 1 2 3 4 5 6 > >> 1 1 1 1 > >> 2 1 1 1 > >> 3 1 1 1 > >> 4 1 1 1 > >> 5 1 1 1 > >> 6 1 1 1 > >> > >> and > >> > >> n 1 2 3 4 5 6 > >> 1 1 1 1 > >> 2 1 1 1 > >> 3 1 1 1 > >> 4 1 1 1 > >> 5 1 1 1 > >> 6 1 1 1 > >> > >> We have no idea whether or not this is actually an easy problem > >> that has > >> already been solved by somebody else. We are just hoping that you > >> can inform > >> us of anything you seem fit, given what we have told you so far. > >> > >> Please let me know if you need any additional information. Thank > >> you in > >> advance! > > jmadden@ics.uci.edu...Obscurium Per Obscurius...www.ics.uci.edu/~jmadden > Joshua O'Madadhain: Information Scientist, Musician, and Philosopher- > At-Tall > It's that moment of dawning comprehension that I live for--Bill > Watterson > My opinions are too rational and insightful to be those of any > organization. > > _____________________________________________________________________ > 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.