Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hierarchical mutual information for the comparison of hierarchical
  community structures in complex networks   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
consistency, robustness and temporal evolution of the hierarchical modular
structure of networks.

16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex