<p>In the last decade, community detection in networks has seen significant progress, marked by the rapid development of advanced algorithms. A major task in this field is to assess the performance of community detection algorithms, which is frequently done on artificial benchmark modular graphs. While the widely adopted Lancichinetti–Fortunato–Radicchi (LFR) benchmark has contributed significantly to the field, its limitations, such as unstable modularity structures, necessitate alternatives attempt. Here, we introduce the General Modular Graph (GMG) model, a versatile and efficient framework for generating realistic artificial networks. With just five parameters—<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12652_2025_4988_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\(\ell \)</EquationSource> </InlineEquation> (number of modules), <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12652_2025_4988_Article_IEq2.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="34" /> </InlineMediaObject> <EquationSource Format="TEX">\(n_{\max }\)</EquationSource> </InlineEquation> (maximum module size), <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12652_2025_4988_Article_IEq3.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="31" /> </InlineMediaObject> <EquationSource Format="TEX">\(n_{\min }\)</EquationSource> </InlineEquation> (minimum module size), <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12652_2025_4988_Article_IEq4.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(o_n\)</EquationSource> </InlineEquation> (number of overlapping nodes), and <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12652_2025_4988_Article_IEq5.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mu \)</EquationSource> </InlineEquation> (mixing parameter)—GMG produces networks with intricate features, including community and anti-community structures, weighted edges, and power-law distributions for degrees and community sizes. GMG outperforms LFR in stability, computational efficiency, and adaptability, supporting overlapping communities and scale-free properties. Its ability to emulate real-world network characteristics establishes GMG as a robust platform for benchmarking community detection algorithms, particularly in overlapping and weighted networks.</p>

General Modular Graphs: a benchmark network model for testing community detection algorithms

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发表日期：

2025年7月29日

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Abhinav Kumar,
Pawan Kumar,
Ravins Dohare

摘要

In the last decade, community detection in networks has seen significant progress, marked by the rapid development of advanced algorithms. A major task in this field is to assess the performance of community detection algorithms, which is frequently done on artificial benchmark modular graphs. While the widely adopted Lancichinetti–Fortunato–Radicchi (LFR) benchmark has contributed significantly to the field, its limitations, such as unstable modularity structures, necessitate alternatives attempt. Here, we introduce the General Modular Graph (GMG) model, a versatile and efficient framework for generating realistic artificial networks. With just five parameters— \(\ell \) (number of modules), \(n_{\max }\) (maximum module size), \(n_{\min }\) (minimum module size), \(o_n\) (number of overlapping nodes), and \(\mu \) (mixing parameter)—GMG produces networks with intricate features, including community and anti-community structures, weighted edges, and power-law distributions for degrees and community sizes. GMG outperforms LFR in stability, computational efficiency, and adaptability, supporting overlapping communities and scale-free properties. Its ability to emulate real-world network characteristics establishes GMG as a robust platform for benchmarking community detection algorithms, particularly in overlapping and weighted networks.