Most of the current complex networks that are of interest to practitioners possess a certain community structure that plays an important role in understanding the properties of these networks. For instance, a closely connected social communities exhibit faster rate of transmission of information in comparison to loosely connected communities. Moreover, many machine learning algorithms and tools that are developed for complex networks try to take advantage of the existence of communities to improve their performance or speed. As a result, there are many competing algorithms for detecting communities in large networks. Unfortunately, these algorithms are often quite sensitive and so they cannot be fine-tuned for a given, but a constantly changing, real-world network at hand. It is therefore important to test these algorithms for various scenarios that can only be done using synthetic graphs that have built-in community structure, power law degree distribution, and other typical properties observed in complex networks. The standard and extensively used method for generating artificial networks is the LFR graph generator. Unfortunately, this model has some scalability limitations and it is challenging to analyze it theoretically. Finally, the mixing parameter μ, the main parameter of the model guiding the strength of the communities, has a non-obvious interpretation and so can lead to unnaturally defined networks. In this paper, we provide an alternative random graph model with community structure and power law distribution for both degrees and community sizes, the Artificial Benchmark for Community Detection (ABCD graph). The model generates graphs with similar properties as the LFR one, and its main parameter ξ can be tuned to mimic its counterpart in the LFR model, the mixing parameter μ. We show that the new model solves the three issues identified above and more. In particular, we test the speed of our algorithm and do a number of experiments comparing basic properties of both ABCD and LFR. The conclusion is that these models produce graphs with comparable properties but ABCD is fast, simple, and can be easily tuned to allow the user to make a smooth transition between the two extremes: pure (independent) communities and random graph with no community structure.

中文翻译：

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社区检测的人工基准（ABCD）——具有社区结构的快速随机图模型

从业者感兴趣的当前大多数复杂网络都具有一定的社区结构，在理解这些网络的属性方面起着重要作用。例如，与松散联系的社区相比，紧密联系的社会社区表现出更快的信息传输速度。此外，为复杂网络开发的许多机器学习算法和工具都试图利用社区的存在来提高其性能或速度。因此，在大型网络中存在许多用于检测社区的竞争算法。不幸的是，这些算法通常非常敏感，因此无法针对给定但不断变化的现实世界网络进行微调。因此，针对各种场景测试这些算法非常重要，这些场景只能使用具有内置社区结构、幂律度分布和在复杂网络中观察到的其他典型属性的合成图来完成。生成人工网络的标准且广泛使用的方法是 LFR 图生成器。不幸的是，这个模型有一些可扩展性的限制，从理论上分析它是有挑战性的。最后是混合参数 该模型存在一些可扩展性限制，理论上对其进行分析具有挑战性。最后是混合参数 该模型存在一些可扩展性限制，理论上对其进行分析具有挑战性。最后是混合参数μ，指导社区强度的模型的主要参数，具有不明显的解释，因此可能导致不自然定义的网络。在本文中，我们提供了另一种具有社区结构和幂律分布的随机图模型，即社区检测的人工基准（ABCD 图）。该模型生成的图形具有与 LFR 相似的属性及其主要参数ξ可以调整以模仿 LFR 模型中的对应物，即混合参数μ. 我们表明，新模型解决了上述三个问题以及更多问题。特别是，我们测试了算法的速度，并进行了一些比较 ABCD 和 LFR 基本属性的实验。结论是这些模型生成的图具有可比较的属性，但 ABCD 快速、简单，并且可以轻松调整以允许用户在两​​个极端之间进行平滑过渡：纯（独立）社区和没有社区结构的随机图。