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Re: avg. geodesic

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Fri, 10 Dec 2004 10:09:15 +0900

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 ```***** To join INSNA, visit http://www.insna.org ***** We should check the process getting [ln(n)/ln(avg.degree) ~ average geodesic]. I referenced     Mark Newman - Random Graphs as Models of Networks     http://www.santafe.edu/research/publications/wpabstract/200202005 . z = avg. degree 1. the mean number of first neighbors of a vertex = z     the mean number of second neighbors of a vertex ~ z^2     the mean number of mth neighbors of a vertex ~ z^m 2. I quote from upper article.     "When the total number of vertices within distance m is equal to the size n of the whole graph, m is equal to the so-called "radius" rof the network around vertex A. ...omited... r (=radius) is thus also approximately equal to the average vertex-vertex distance L". 3. z^m ~ n => m ~ ln(n)/ln(z) Every steps used some rough approximations (as like many statistical physics' applications) The "mean" in step 1 is rough approximation (the reference seemed to say nothing about that's accurate distribution. Only mean was mentioned.) In step 2, 3 there is a clear approximation. Due to many approximations, maybe the given equation seems to be valid when 'order (rough value)' is considered, not 'accurate value'. Maybe I could miss something. If there are mistakes, let me know. Best Regards. Kim Se Kwon. ----- Original Message ----- From: "[log in to unmask]" <[log in to unmask]> To: <[log in to unmask]> Sent: Thursday, December 09, 2004 6:38 PM Subject: Re: avg. geodesic > ***** To join INSNA, visit http://www.insna.org ***** > > Hi > > I made a few experiments myself. I created in Pajek 5 Random Erdos-Renyi > Undirected General Graphs with n=100, and avg. degree=3, and calclulated > their avg. geodesic distance with Pajek>Net>Paths between 2 > vertices->Distribution of Distances->from all vertices. Results range from > 3.69 to 4.62, i.e. they hover around the predicted 4.191 with quite some > variability. > > Then I did the same for the network parameters I am interested in, i.e. > n=418 avg. degree=87. For all 5 networks I get an avg. geodesic of > 1.79etc, which is consistently different from the predicted 1.35. > Could it be that the ln(n)/ln(avg.degree) formula applies only to sparse > networks? > > > Thanks, > > Gianluca > > > > Did you make a Random Erdos-Renyi Undirected General Graph? > > > > The approximation you gave may be applied to only random ER graph. (there > > are more general approxiations that can be applied more general graph). > > > > And you get the average distance of graph using Net->Paths between 2 > > vertices->Distribution of Distances->from all vertices menu. > > > > I did two experiments. > > > > 1. 100 nodes, average degree 3. > > approximation : ln(100)/ln(3)=4.191, real : 4.41981 > > 2. 1000 nodes, average degree 5. > > approximation : ln(1000)/ln(5)=4.292, real : 4.48113 > > > > Is it almost same? > > > > Best. > > > > ----- Original Message ----- > > From: "[log in to unmask]" <[log in to unmask]> > > To: <[log in to unmask]> > > Sent: Tuesday, December 07, 2004 9:07 PM > > > > > > > ***** To join INSNA, visit http://www.insna.org ***** > > > > > > Hi everybody, > > > > > > The avg. geodesic distance in a (connected) random network is approximated > > by ln(n)/ln(k), where n=number_of_nodes , and k=avg._ties_per_node. However, > > if I create a random network with parameters n and k in Pajek and calcluate > > its avg. geodesic distance, I get sizeably different results (regardless of > > how large I set n). Any idea what I could be doing wrong? > > > > > > > > > Thanks, > > > > > > Gianluca > > > > > > > > > PS: To calculate the avg. geodesic distance I've been using > > > Ucinet/network/cohesion/distance -->adjacency > > > > > > > > > > > > > > > > > > ____________________________________________________________ > > > Libero ADSL: 3 mesi gratis e navighi a 1.2 Mega, senza costi di > > attivazione. > > > Abbonati subito su http://www.libero.it > > > > > > _____________________________________________________________________ > > > 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. > > > > > > > > > Gianluca Carnabuci > PhD candidate > University of Twente > > P.O. Box 217 > Enschede > The Netherlands > > Ph: 0031 53 4892352 > > > > ____________________________________________________________ > Libero ADSL: 3 mesi gratis e navighi a 1.2 Mega, senza costi di attivazione. > Abbonati subito su http://www.libero.it > > _____________________________________________________________________ > 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.```