Open AccessOn the Number of Non-Zero Elements of Joint Degree Vectors
Author(s) -
Éva Czabarka,
Johannes Rauh,
Kayvan Sadeghi,
Taylor Short,
László Á. Székely
Publication year - 2017
Publication title -
the electronic journal of combinatorics/the journal of combinatorics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.703
H-Index - 52
eISSN - 1097-1440
pISSN - 1077-8926
DOI - 10.37236/6385
Subject(s) - mathematics , combinatorics , degree (music) , vertex (graph theory) , joint probability distribution , upper and lower bounds , graph , discrete mathematics , zero (linguistics) , joint (building) , random graph , exponential function , statistics , mathematical analysis , linguistics , physics , acoustics , architectural engineering , engineering , philosophy
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.