The number one criticism of average-case analysis is that we do not actually know the probability distribution of real-world inputs. Thus, analyzing an algorithm on some random model has no implications for practical performance. At its core, this criticism doubts the existence of external validity; i.e., it assumes that algorithmic behavior on the somewhat simple and clean models does not translate beyond the models to practical performance real-world input.

With this article, we provide a first step toward studying the question of external validity systematically. To this end, we evaluate the performance of six graph algorithms on a collection of 2,740 sparse real-world networks depending on two properties: heterogeneity (variance in the degree distribution) and locality (tendency of edges to connect vertices that are already close). We compare this with the performance on generated networks with varying locality and heterogeneity. We find that the performance in the idealized setting of network models translates surprisingly well to real-world networks. Moreover, heterogeneity and locality appear to be the core properties impacting the performance of many graph algorithms.

对平均情况分析的第一个批评是我们实际上并不知道现实世界输入的概率分布。因此，在某些随机模型上分析算法对实际性能没有影响。从本质上讲，这种批评怀疑外部有效性的存在；即，它假设稍微简单和干净的模型上的算法行为不会超出模型转化为实际性能的现实世界输入。

通过这篇文章，我们为系统地研究外部效度问题迈出了第一步。为此，我们根据两个属性评估六种图算法在 2,740 个稀疏现实世界网络上的性能：异质性（度分布的方差）和局部性（边连接已经接近的顶点的倾向）。我们将其与具有不同局部性和异构性的生成网络的性能进行比较。我们发现网络模型的理想化设置中的性能令人惊讶地很好地转化为现实世界的网络。此外，异构性和局部性似乎是影响许多图算法性能的核心属性。