On the Number of Non-Zero Elements of Joint Degree Vectors | Zendy

Éva Czabarka | Zendy; Johannes Rauh | Zendy; Kayvan Sadeghi | Zendy; Taylor Short | Zendy; László Á. Székely | Zendy

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On 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

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.

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