We propose a randomized parameter-oblivious algorithm that, given query access to a graph $G$ with arboricity $α$, and average degree $d$, makes $\widetilde{O}\left(\fracα{\varepsilon^2d}\right)$ Degree and $\widetilde{O}\left(\frac{1}{\varepsilon^2}\right)$ RandEdge queries to obtain an estimate $\widehat{d}$ satisfying $\widehat{d} \in (1\pm\varepsilon)d$. This also yields an algorithm that uses $\widetilde{O}\left(\frac{1}{\varepsilon^2}\min(d,\fracα{d})\right)$ Degree and RandEdge queries. This improves the $\widetilde{O}_{\varepsilon,\log n}(\frac{1}{\varepsilon^2}$ $\min(d,\sqrt{\frac{n}{d}}))$ query algorithm of [Beretta et al., SODA 2026] that has access to Degree, Neighbour, and RandEdge queries. We show that any algorithm that has access to Degree, Neighbour, and RandEdge queries, must make at least $Ω\left(\min\left(d,\fracα{d}\right)\right)$ queries, even with the knowledge of $n$ and $α$. Even with Pair and FullNbr queries, an algorithm must make $Ω\left(\min\left(d,\fracα{d}\right)\right)$ queries for certain ranges of $α$. When $n$ is unknown, any algorithm with access to all the queries discussed above must make $Ω\left(\min\left(d,\fracα{d}\right)\right)$ queries. We also establish that any sublinear algorithm using Degree and RandEdge queries must make at least $Ω(\frac{1}{\varepsilon})$ RandEdge queries. Furthermore, any algorithm having access to Degree, FullNbr, and RandEdge queries that makes $o(\frac{1}{\varepsilon^2})$ RandEdge queries must make $Ω(\fracα{\varepsilon^2d})$ Degree and FullNbr queries. This settles the query complexity of estimating average degree using Degree and FullNbr queries.

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