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Hierarchical mutual information for the comparison of hierarchical community structures in complex networks

Overview of attention for article published in Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, December 2015
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About this Attention Score

  • In the top 25% of all research outputs scored by Altmetric
  • High Attention Score compared to outputs of the same age (91st percentile)
  • High Attention Score compared to outputs of the same age and source (93rd percentile)

Mentioned by

twitter
37 tweeters

Citations

dimensions_citation
9 Dimensions

Readers on

mendeley
60 Mendeley
Title
Hierarchical mutual information for the comparison of hierarchical community structures in complex networks
Published in
Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, December 2015
DOI 10.1103/physreve.92.062825
Pubmed ID
Authors

Juan Ignacio Perotti, Claudio Juan Tessone, Guido Caldarelli

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 hierarchical mutual information, which is a generalization of the traditional mutual information and makes it possible to compare hierarchical partitions and hierarchical community structures. The 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 consistency, robustness, and temporal evolution of the hierarchical modular structure of networks.

Twitter Demographics

The data shown below were collected from the profiles of 37 tweeters who shared this research output. Click here to find out more about how the information was compiled.

Mendeley readers

The data shown below were compiled from readership statistics for 60 Mendeley readers of this research output. Click here to see the associated Mendeley record.

Geographical breakdown

Country Count As %
United Kingdom 3 5%
United States 3 5%
Switzerland 2 3%
Brazil 1 2%
Japan 1 2%
Italy 1 2%
Netherlands 1 2%
Unknown 48 80%

Demographic breakdown

Readers by professional status Count As %
Student > Ph. D. Student 24 40%
Researcher 12 20%
Professor > Associate Professor 6 10%
Professor 5 8%
Student > Master 4 7%
Other 9 15%
Readers by discipline Count As %
Computer Science 13 22%
Physics and Astronomy 12 20%
Unspecified 9 15%
Agricultural and Biological Sciences 7 12%
Engineering 6 10%
Other 13 22%

Attention Score in Context

This research output has an Altmetric Attention Score of 19. This is our high-level measure of the quality and quantity of online attention that it has received. This Attention Score, as well as the ranking and number of research outputs shown below, was calculated when the research output was last mentioned on 14 January 2016.
All research outputs
#616,210
of 11,421,287 outputs
Outputs from Physical Review E: Statistical, Nonlinear, and Soft Matter Physics
#75
of 5,614 outputs
Outputs of similar age
#19,368
of 234,315 outputs
Outputs of similar age from Physical Review E: Statistical, Nonlinear, and Soft Matter Physics
#4
of 59 outputs
Altmetric has tracked 11,421,287 research outputs across all sources so far. Compared to these this one has done particularly well and is in the 94th percentile: it's in the top 10% of all research outputs ever tracked by Altmetric.
So far Altmetric has tracked 5,614 research outputs from this source. They receive a mean Attention Score of 2.2. This one has done particularly well, scoring higher than 98% of its peers.
Older research outputs will score higher simply because they've had more time to accumulate mentions. To account for age we can compare this Altmetric Attention Score to the 234,315 tracked outputs that were published within six weeks on either side of this one in any source. This one has done particularly well, scoring higher than 91% of its contemporaries.
We're also able to compare this research output to 59 others from the same source and published within six weeks on either side of this one. This one has done particularly well, scoring higher than 93% of its contemporaries.