Communicability angles reveal critical edges for network consensus dynamics

Effective approach to epidemic containment using link equations in complex networks

Epidemic containment is a major concern when confronting large-scale infections in complex networks. Many studies have been devoted to analytically understand how to restructure the network to minimize the impact of major outbreaks of infections at large scale. In many cases, the strategies are based on isolating certain nodes, while less attention has been paid to interventions on the links. In epidemic spreading, links inform about the probability of carrying the contagion of the disease from infected to susceptible individuals. Note that these states depend on the full structure of the network, and its determination is not straightforward from the knowledge of nodes' states. Here, we confront this challenge and propose a set of discrete-time governing equations that can be closed and analyzed, assessing the contribution of links to spreading processes in complex networks. Our approach allows a scheme for the containment of epidemics based on deactivating the most important links in transmitting the disease. The model is validated in synthetic and real networks, yielding an accurate determination of epidemic incidence and critical thresholds. Epidemic containment based on link deactivation promises to be an effective tool to maintain functionality of networks while controlling the spread of diseases, such as disease spread through air transportation networks.

Scaling in topological properties of brain networks

The organization in brain networks shows highly modular features with weak inter-modular interaction. The topology of the networks involves emergence of modules and sub-modules at different levels of constitution governed by fractal laws that are signatures of self-organization in complex networks. The modular organization, in terms of modular mass, inter-modular, and intra-modular interaction, also obeys fractal nature. The parameters which characterize topological properties of brain networks follow one parameter scaling theory in all levels of network structure, which reveals the self-similar rules governing the network structure. Further, the calculated fractal dimensions of brain networks of different species are found to decrease when one goes from lower to higher level species which implicates the more ordered and self-organized topography at higher level species. The sparsely distributed hubs in brain networks may be most influencing nodes but their absence may not cause network breakdown, and centrality parameters characterizing them also follow one parameter scaling law indicating self-similar roles of these hubs at different levels of organization in brain networks. The local-community-paradigm decomposition plot and calculated local-community-paradigm-correlation co-efficient of brain networks also shows the evidence for self-organization in these networks.