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)
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Abstract
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.
| Item Type: | Article |
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| Identification Number: | 10.1103/PhysRevE.92.062825 |
| Additional Information: | The paper was accepted for publication subject minor revisions. Together with the paper, a software python package was released under the GPL licence 2 (1991), useful for the computation of the hierarchical mutual information. |
| Projects: | MULTIPLEX, SIMPOL, DOLFINS |
| Subjects: | H Social Sciences > HA Statistics H Social Sciences > HG Finance Q Science > Q Science (General) Q Science > QA Mathematics Q Science > QA Mathematics > QA75 Electronic computers. Computer science Q Science > QC Physics |
| Research Area: | Computer Science and Applications |
| Depositing User: | Users 61 not found. |
| Date Deposited: | 16 Nov 2015 08:48 |
| Last Modified: | 02 Feb 2016 14:40 |
| URI: | http://eprints.imtlucca.it/id/eprint/2897 |
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