Comparison and validation of community structures in complex networks.pdfVIP

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