Multifractal analysis on gene and PPI networks
Danling Wang1, Yanfei Wang2
1School of Mathematics and Physics, University of Science and Technology, Beijing, China
2School of Sciences China Agricultural University Tsinghuadonglu 17, 100083, Beijing, China
Multifractal analysis is a useful way to systematically describe the spatial heterogeneity of both theoretical and experimental fractal patterns. In this paper, we introduce a new box-covering algorithm to compute the generalized fractal dimensions of complex networks. We apply our method on networks built on disease-related gene microarray data and PPI networks. For each microarray data, we compare the difference of multifractal behaviour between gene networks that reconstructed from patients and normal micorarrays. The result suggests that multifractality exists in all the gene networks we generated and the differences in the shape of the Dq curves are obvious for all microarray data sets. Meanwhile, multifractal analysis could provide a potentially useful tool for gene clustering and identification between healthy people and patients. For the analysis of PPI networks, the results support that the algorithm is a suitable and effective tool to perform multifractal analysis of complex networks, and this method can be a useful tool to cluster and classify real PPI networks of organisms.