Artificial Benchmark for Community Detection (ABCD)—Fast random graph model with community structure

Abstract

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.

Survey of Generative Methods for Social Media Analysis

“…As a result, it became a standard and extensively used method for generating artificial networks. An alternative, "LFR-like" random graph model, the Artificial Benchmark for Community Detection (ABCD graph) [132] was recently introduced and implemented 22 . The authors of [132] continue working on the model, currently working on the implementation that uses multiple threads (ABCDe) 23 .…”

“…An alternative, "LFR-like" random graph model, the Artificial Benchmark for Community Detection (ABCD graph) [132] was recently introduced and implemented 22 . The authors of [132] continue working on the model, currently working on the implementation that uses multiple threads (ABCDe) 23 . LFR and ABCD produce graphs with comparable properties but ABCD is faster than LFR (ABCDe is even faster than ABCD) 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.…”

Modularity of the ABCD Random Graph Model with Community Structure

“…In this paper, we analyze the Artificial Benchmark for Community Detection (ABCD graph) [23] that was recently introduced and implemented * , including a fast implementation that uses multiple threads (ABCDe) † . Undirected variant of LFR and ABCD produce graphs with comparable properties but ABCD/ABCDe is faster than LFR and can be easily tuned to allow the user to make a smooth transition between the two extremes: pure (disjoint) communities and random graph with no community structure.…”

A Configuration Model with Triadic Closure

“…Since the CTC model has communities, one application of our model is that it can be used as a benchmark for community detection algorithms. Other models that were often used to benchmark community detection algorithms include stochastic block models [12], [13], LFR models [14], [15] and ABCD models [16]. We remark that it is not clear if the models above possess all the five fundamental properties.…”

“…The three community detection algorithms are the walktrap algorithm[18], the leading eigenvectors algorithm[19] and the fast unfolding algorithm[20]. We compare the community detection of the CTC model with that of the ABCD network[16] and that of the LFR network[14]. Source code to generate ABCD networks and LFR networks has been provided in the github.To make a fair comparison, the three network models must have the same degree sequences or distributions.…”