کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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419007 | 681731 | 2015 | 6 صفحه PDF | دانلود رایگان |
The joint degree matrix of a graph gives the number of edges between vertices of degree ii and degree jj for every pair (i,j)(i,j). One can perform restricted swap operations to transform a graph into another with the same joint degree matrix. We prove that the space of all realizations of a given joint degree matrix over a fixed vertex set is connected via these restricted swap operations. This was claimed before, but there is a flaw in the proof, which we illustrate by example. We also give a simplified proof of the necessary and sufficient conditions for a matrix to be a joint degree matrix, which includes a general method for constructing realizations. Finally, we address the corresponding MCMC methods to sample uniformly from these realizations.
Journal: Discrete Applied Mathematics - Volume 181, 30 January 2015, Pages 283–288