Estimating the average degree of graph is a classic problem in sublinear graph algorithm. Eden, Ron, and Seshadhri (ICALP 2017, SIDMA 2019) gave a simple algorithm for this problem whose running time depended on the graph arboricity, but the underlying simplicity and associated analysis were buried inside the main result. Moreover, the description there loses logarithmic factors because of parameter search. The aim of this note is to give a full presentation of this algorithm, without these losses. Consider standard access (vertex samples, degree queries, and neighbor queries) to a graph $G = (V,E)$ of arboricity at most $α$. Let $d$ denote the average degree of $G$. We describe an algorithm that gives a $(1+\varepsilon)$-approximation to $d$ degree using $O(\varepsilon^{-2}α/d)$ queries. For completeness, we modify the algorithm to get a $O(\varepsilon^{-2} \sqrt{n/d})$ query

翻译：估计图的平均度是亚线性图算法中的一个经典问题。Eden、Ron 和 Seshadhri（ICALP 2017, SIDMA 2019）为此问题给出一个简单算法，其运行时间依赖于图的树状度，但该算法的简洁性及相应分析被湮没于其主要结果中。此外，由于参数搜索，该描述存在对数因子的损失。本文旨在给出该算法的完整呈现，避免这些损失。考虑对树状度至多为 $α$ 的图 $G = (V,E)$ 进行标准访问（顶点采样、度数查询和邻居查询）。令 $d$ 表示 $G$ 的平均度。我们描述一个算法，使用 $O(\varepsilon^{-2}α/d)$ 次查询即可得到 $d$ 的 $(1+\varepsilon)$-近似值。为完备起见，我们修改该算法以获得 $O(\varepsilon^{-2} \sqrt{n/d})$ 次查询的结果。