Geodesic
On the number of non-zero elements of joint degree vectors
Éva Czabarka1 ; Johannes Rauh2 ; Kayvan Sadeghi3 ; Taylor Short4 ; László Székely1
1Department of Mathematics University of South Carolina Columbia, SC, U.S.A
2Max Planck Institute for Mathematics in the Sciences Leipzig, Germany
3Statistical Laboratory University of Cambridge Cambridge, United Kingdom
4Grand Valley State University
The electronic journal of combinatorics, Tome 24 (2017) no. 1
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Joint degree vectors give the number of edges between vertices of degree $i$ and degree $j$ for $1\le i\le j\le n-1$ 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.
DOI : 10.37236/6385
Classification : 05C80, 05C07
Mots-clés : degree sequence, joint degree distribution, joint degree vector, joint degree matrix, exponential random graph model

Éva Czabarka  1   ; Johannes Rauh  2   ; Kayvan Sadeghi  3   ; Taylor Short  4   ; László Székely  1

1 Department of Mathematics University of South Carolina Columbia, SC, U.S.A
2 Max Planck Institute for Mathematics in the Sciences Leipzig, Germany
3 Statistical Laboratory University of Cambridge Cambridge, United Kingdom
4 Grand Valley State University 
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Éva Czabarka; Johannes Rauh; Kayvan Sadeghi; Taylor Short; László Székely. On the number of non-zero elements of joint degree vectors. The electronic journal of combinatorics, Tome 24 (2017) no. 1. doi: 10.37236/6385

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