Rich-club vs rich-multipolarization phenomena in weighted networks

Large scale hierarchies characterize complex networks in different domains. Elements at their top, usually the most central or influential, may show multipolarization or tend to club forming tightly interconnected communities. The rich-club phenomenon quantified this tendency based on unweighted network representations. Here, we define this metric for weighted networks and discuss the appropriate normalization which preserves nodes' strengths and discounts structural strength-strength correlations if present. We find that in some real networks the results given by the weighted rich-club coefficient can be in sharp contrast to the ones in the unweighted approach. We also discuss that the scanning of the weighted subgraphs formed by the high-strength hubs is able to unveil features contrary to the average: the formation of local alliances in rich-multipolarized environments, or a lack of cohesion even in the presence of rich-club ordering. Beyond structure, this analysis matters for understanding correctly functionalities and dynamical processes relying on hub interconnectedness.Comment: 12 pages, 2 figure

Essential plasticity and redundancy of metabolism unveiled by synthetic lethality analysis

We unravel how functional plasticity and redundancy are essential mechanisms underlying the ability to survive of metabolic networks. We perform an exhaustive computational screening of synthetic lethal reaction pairs in Escherichia coli in a minimal medium and we find that synthetic lethal pairs divide in two different groups depending on whether the synthetic lethal interaction works as a backup or as a parallel use mechanism, the first corresponding to essential plasticity and the second to essential redundancy. In E. coli, the analysis of pathways entanglement through essential redundancy supports the view that synthetic lethality affects preferentially a single function or pathway. In contrast, essential plasticity, the dominant class, tends to be inter-pathway but strongly localized and unveils Cell Envelope Biosynthesis as an essential backup for Membrane Lipid Metabolism. When comparing E. coli and Mycoplasma pneumoniae, we find that the metabolic networks of the two organisms exhibit a large difference in the relative importance of plasticity and redundancy which is consistent with the conjecture that plasticity is a sophisticated mechanism that requires a complex organization. Finally, coessential reaction pairs are explored in different environmental conditions to uncover the interplay between the two mechanisms. We find that synthetic lethal interactions and their classification in plasticity and redundancy are basically insensitive to medium composition, and are highly conserved even when the environment is enriched with nonessential compounds or overconstrained to decrease maximum biomass formation.Comment: 22 pages, 4 figure

Navigability of temporal networks in hyperbolic space

Information routing is one of the main tasks in many complex networks with a communication function. Maps produced by embedding the networks in hyperbolic space can assist this task enabling the implementation of efficient navigation strategies. However, only static maps have been considered so far, while navigation in more realistic situations, where the network structure may vary in time, remain largely unexplored. Here, we analyze the navigability of real networks by using greedy routing in hyperbolic space, where the nodes are subject to a stochastic activation-inactivation dynamics. We find that such dynamics enhances navigability with respect to the static case. Interestingly, there exists an optimal intermediate activation value, which ensures the best trade-off between the increase in the number of successful paths and a limited growth of their length. Contrary to expectations, the enhanced navigability is robust even when the most connected nodes inactivate with very high probability. Finally, our results indicate that some real networks are ultranavigable and remain highly navigable even if the network structure is extremely unsteady. These findings have important implications for the design and evaluation of efficient routing protocols that account for the temporal nature of real complex networks.Comment: 10 pages, 4 figures. Includes Supplemental Informatio