relation: http://eprints.imtlucca.it/2897/
title: Hierarchical mutual information for the comparison of hierarchical community structures in complex networks
creator: Perotti, Juan I.
creator: Tessone, Claudio Juan
creator: Caldarelli, Guido
subject: HA Statistics
subject: HG Finance
subject: Q Science (General)
subject: QA Mathematics
subject: QA75 Electronic computers. Computer science
subject: QC Physics
description: The quest for a quantitative characterization of community and modular structure of complex networks produced a variety of methods and algorithms to classify different networks. However, it is not clear if such methods provide consistent, robust and meaningful results when considering hierarchies as a whole. Part of the problem is the lack of a similarity measure for the comparison of hierarchical community structures. In this work we give a contribution by introducing the {\it hierarchical mutual information}, which is a generalization of the traditional mutual information, and allows to compare hierarchical partitions and hierarchical community structures. The {\it normalized} version of the hierarchical mutual information should behave analogously to the traditional normalized mutual information. Here, the correct behavior of the hierarchical mutual information is corroborated on an extensive battery of numerical experiments. The experiments are performed on artificial hierarchies, and on the hierarchical community structure of artificial and empirical networks. Furthermore, the experiments illustrate some of the practical applications of the hierarchical mutual information. Namely, the comparison of different community detection methods, and the study of the the consistency, robustness and temporal evolution of the hierarchical modular structure of networks.
publisher: American Physical Society
date: 2015-12
type: Article
type: PeerReviewed
format: application/pdf
language: en
rights: cc_by_nc_nd
identifier: http://eprints.imtlucca.it/2897/1/1508.04388v1.pdf
identifier:   Perotti, Juan I. and Tessone, Claudio Juan and Caldarelli, Guido  Hierarchical mutual information for the comparison of hierarchical community structures in complex networks.  Physical Review E (92).  062825.  ISSN 1539-3755      (2015)  
relation: http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.062825
relation: 10.1103/PhysRevE.92.062825