Artificial benchmark for community detection with outliers (ABCD+o)
Bogumił Kamiński, Paweł Prałat, François Théberge
Abstract
Abstract The A rtificial B enchmark for C ommunity D etection graph ( ABCD ) is a random graph model with community structure and power-law distribution for both degrees and community sizes. The model generates graphs with similar properties as the well-known LFR one, and its main parameter $$\xi$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ξ</mml:mi> </mml:math> can be tuned to mimic its counterpart in the LFR model, the mixing parameter $$\mu$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>μ</mml:mi> </mml:math> . In this paper, we extend the ABCD model to include potential outliers. We perform some exploratory experiments on both the new ABCD+o model as well as a real-world network to show that outliers pose some distinguishable properties. This ensures that our new model may serve as a benchmark of outlier detection algorithms.