On the number of non-zero elements of joint degree vectors
The Electronic Journal of Combinatorics
Electronic Journal of Combinatorics
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Czabarka, É., Sadeghi, K., Rauh, J., Short, T., & Székely, L. (2017). On the number of non-zero elements of joint degree vectors. The Electronic Journal of Combinatorics, 24 (1. #P1.55)https://doi.org/10.17863/CAM.9500
Joint degree vectors give the number of edges between vertices of degree i and degree j for 1 ≤ i ≤ j ≤ n-1 in an n-vertex graph. We find lower and upper bounds for the maximum number of nonzero elements in a joint degree vector as a function of n. This provides an upper bound on the number of estimable parameters in the exponential random graph model with bidegree-distribution as its sufficient statistics.
degree sequence, joint degree distribution, joint degree vector, joint degree matrix, bidegree distribution, exponential random graph model
All authors except the second author were supported in part by the U.S. Air Force Office of Scientic Research (AFOSR) and the Defense Advanced Research Projects Agency (DARPA). The last author was supported in part by the NSF DMS contracts no.1300547 and 1600811.
This record's DOI: https://doi.org/10.17863/CAM.9500
This record's URL: https://www.repository.cam.ac.uk/handle/1810/264143