No, N is the number of authors in the respective graph. The main graph currently entails 45,594 people. Let me illustrate the results with an example. Assume some author is located at an average distance of 4 from other authors in the graph. Then the total distance is: sum d = 45594 * 4 = 182376. Plugging this into the closeness formula, C = 1 / sum d, produces a closeness value of 1 / 182376 = 5.483178e-06. Transforming it to the former CollEc's definition means multiplying it by (sum d)^2 / N: (182376^2 / 45594) * 5.483178e-06 = 4. Christian Düben Research Associate Chair of Macroeconomics Hamburg University Von-Melle-Park 5, Room 3102 20146 Hamburg Germany +49 40 42838 1898 christian.dueben@uni-hamburg.de http://www.christian-dueben.com -----Original Message----- From: Christian Zimmermann <zimmermann@stlouisfed.org> Sent: Mittwoch, 30. Dezember 2020 16:22 To: Düben, Christian <Christian.Dueben@uni-hamburg.de> Cc: Thomas Krichel <krichel@openlib.org>; CollEc Run <collec-run@lists.openlib.org> Subject: Re: [CollEc] CollEc App Offline And N would happen to be close to a million? Christian Zimmermann FIGUGEGL! Economic Research Federal Reserve Bank of St. Louis P.O. Box 442 St. Louis MO 63166-0442 USA https://ideas.repec.org/zimm/ @CZimm_economist On Wed, 30 Dec 2020, D�ben, Christian wrote:
I do use binary paths here. Weighted paths are not exported.
As far as I understand it, there is one fixed closeness formula: 1 / (sum d). Just like the definitions of the mean, the variance, and other statistical measures are fixed. Your alternative measure appears to be (sum d) / N. Thus, multiplying my results by d^2 / N should produce your results. This is not about different path defintions. The former CollEc's closeness values are simply a scaled version of the new CollEc's closeness values. How does this make my results counter-intuitive? There is nothing different about the underlying paths.
Christian D�ben Research Associate Chair of Macroeconomics Hamburg University Von-Melle-Park 5, Room 3102 20146 Hamburg Germany +49 40 42838 1898 christian.dueben@uni-hamburg.de http://www.christian-dueben.com
-----Original Message----- From: Thomas Krichel <krichel@openlib.org> Sent: Mittwoch, 30. Dezember 2020 04:27 To: D�ben, Christian <Christian.Dueben@uni-hamburg.de> Cc: CollEc Run <collec-run@lists.openlib.org> Subject: Re: [CollEc] CollEc App Offline
D�ben, Christian writes
Thomas, how do you get closeness values larger than 1?
I use common sense. The closeness of a person is the average distance from one to any other, for all others. Since the distance between any pair is at least one, the average must be larger than one.
Do you scale the results by some factor?
No.
Or is the distance between co-authors not 1 in your case?
It is.
With the closeness equation of C(v) = 1 / (\sum_{i \neq v} d(v, i)) where d(v, i) is the length of the shortest cost path between author v and author i and d(v, i) \geq 1, any closeness value should be between 0 and 1.
There is something counter-intuitive in this approach.
I said many times, if we don't use a binary model, we will leave our users confused. Alternative weighing schemes should be used to filter out from binary short paths that have the same length. However, the way you do that will not have any impact on the closeness, as expressed in my common sense understanding. It will only impact the betweenness.
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Cheers,
Thomas Krichel http://openlib.org/home/krichel skype:thomaskrichel
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