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arXiv · 1511.01035

On the Number of Non-zero Elements of Joint Degree Vectors

Eva Czabarka·Johannes Rauh·Kayvan Sadeghi·Taylor Short·Laszlo A Szekely
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Abstract

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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Eva Czabarka, Johannes Rauh, Kayvan Sadeghi, Taylor Short, Laszlo A Szekely. 2017-02-22. On the Number of Non-zero Elements of Joint Degree Vectors. https://arxiv.org/abs/1511.01035

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