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Comparison and validation of community structures in complex networks.pdf
Comparison and validation of community structures
in complex networks
6
0
0
¨ ∗
2 Mika Gustafsson, Michael Hornquist , Anna Lombardi
n
a Division of Physics and Electronics, Department of Science and Technology, Linkoping
¨
J
University, SE-601 74 Norrkoping, Sweden
¨
0
1
]
h
p Abstract
-
c
o The issue of partitioning a network into communities has attracted a great deal of atten-
s. tion recently. Most authors seem to equate this issue with the one of finding the maximum
s value of the modularity, as defined by Newman. Since the problem formulated this way is
c
i NP-hard, most effort has gone into the construction of search algorithms, and less to the
s
y question of other measures of community structures, similarities between various partition-
h ings and the validation with respect to external information.
p
[ Here we concentrate on a class of computer generated networks and on three well-studied
real networks which constitute a bench-mark for network studies; the karate club, the US
1
v college football teams and a gene network of yeast. We utilize some standard ways of
7 clustering data (originally not designed for finding community structures in networks) and
5
0 show that these classical methods sometimes outperform the newer ones. We discuss var-
1 ious measures of the strength of the modular structure, and show by examples features
0 and drawbacks. Fur
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