Zhao Yang, Juan I. Perotti, Claudio J. Tessone

Hierarchical organization is an important, prevalent characteristic ofcomplex systems; in order to understand their organization, the study of theunderlying (generally complex) networks that describe the interactions betweentheir constituents plays a central role. Numerous previous works have shownthat many real-world networks in social, biologic and technical systems presenthierarchical organization, often in the form of a hierarchy of communitystructures. Many artificial benchmark graphs have been proposed in order totest different community detection methods, but no benchmark has been developedto throughly test the detection of hierarchical community structures. In thisstudy, we fill this vacancy by extending the Lancichinetti-Fortunato-Radicchi(LFR) ensemble of benchmark graphs, adopting the rule of constructinghierarchical networks proposed by Ravasz and Barab\’asi. We employ thisbenchmark to test three of the most popular community detection algorithms, andquantify their accuracy using the traditional Mutual Information and therecently introduced Hierarchical Mutual Information. The results indicate thatthe Ravasz-Barab\’asi-Lancichinetti-Fortunato-Radicchi (RB-LFR) benchmarkgenerates a complex hierarchical structure constituting a challenging benchmarkfor the considered community detection methods.