A broad range of systems spanning biology, technology, and social phenomena may be represented and analyzed as complex networks. Recent studies of such networks using $k$-core decomposition have uncovered groups of nodes that play important roles. Here, we present $s$-core analysis, a generalization of $k$-core (or $k$-shell) analysis to complex networks where the links have different strengths or weights. We demonstrate the $s$-core decomposition approach on two random networks (ER and configuration model with scale-free degree distribution) where the link weights are (i) random, (ii) correlated, and (iii) anticorrelated with the node degrees. Finally, we apply the $s$-core decomposition approach to the protein-interaction network of the yeast Saccharomyces cerevisiae in the context of two gene-expression experiments: oxidative stress in response to cumene hydroperoxide (CHP), and fermentation stress response (FSR). We find that the innermost $s$-cores are (i) different from innermost $k$-cores, (ii) different for the two stress conditions CHP and FSR, and (iii) enriched with proteins whose biological functions give insight into how yeast manages these specific stresses.

• Received 14 March 2013
• Revised 15 November 2013

DOI:https://doi.org/10.1103/PhysRevE.88.062819