Abstract: This article explores the relationship between communities and short cycles in complex networks, based on the fact that nodes more densely connected amongst one another are more likely to be linked through short cycles. By identifying combinations of 3-, 4- and 5-edge-cycles, a subnetwork is obtained which contains only those nodes and links belonging to such cycles, which can then be used to highlight community structure. Examples are shown using a theoretical model (Sznajd networks) and a real-world network (NCAA football).
Abstract: We study the fame distribution of scientists and other social groups as measured by the number of Google hits garnered by individuals in the population. Past studies have found that the fame distribution decays either in power-law [arXiv:cond-mat/0310049] or exponential [Europhys. Lett., 67, (4) 511-516 (2004)] fashion, depending on whether individuals in the social group in question enjoy true fame or not. In our present study we examine critically Google counts as well as the methods of data analysis. While the previous findings are corroborated in our present study, we find that, in most situations, the data available does not allow for sharp conclusions.