Communicability angles reveal critical edges for network consensus dynamics

Estrada, Ernesto; Vargas-Estrada, Eusebio; Ando, Hiroyasu

doi:10.1103/physreve.92.052809

Cited by 11 publications

(8 citation statements)

References 66 publications

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“…Further, as the smaller modules reach the motif level (here triangular motif), each node in the motif has equal importance (similar due to same degree in each node), with single value of C B . If a particular module at any level is considered, C B increases as k , indicating significant important role of hubs in information processing within the module 36 37 38 39 40 . The scaling of C B data for all modules and sub-modules in a particular network follows one parameter scaling law (single power-law-fitted line on the scaled data as shown in Figs 8 and 9 panels C) which reveals similar topological constitution of the network at all modules and sub-modules at various levels of organization of the network.…”

Section: Resultsmentioning

confidence: 99%

Scaling in topological properties of brain networks

Singh

Khundrakpam

Reid

et al. 2016

Sci Rep

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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.

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Section: Resultsmentioning

confidence: 99%

Scaling in topological properties of brain networks

Singh

Khundrakpam

Reid

et al. 2016

Sci Rep

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“…There are many ways of describing what happens to a network when it is damaged or altered [57, 77, 78]. F-scores contribute to this discussion as well because it is sometimes robustness at some target node that is more important than global network stability, and f-scores reveal exactly that.…”

Section: Discussionmentioning

confidence: 99%

Approximating frustration scores in complex networks via perturbed Laplacian spectra

Savol

Chennubhotla

2015

Phys. Rev. E

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Systems of many interacting components, as found in physics, biology, infrastructure, and the social sciences, are often modeled by simple networks of nodes and edges. The real-world systems frequently confront outside intervention or internal damage whose impact must be predicted or minimized, and such perturbations are then mimicked in the models by altering nodes or edges. This leads to the broad issue of how to best quantify changes in a model network after some type of perturbation. In the case of node removal there are many centrality metrics which associate a scalar quantity with the removed node, but it can be difficult to associate the quantities with some intuitive aspect of physical behavior in the network. This presents a serious hurdle to the application of network theory: real-world utility networks are rarely altered according to theoretic principles unless the kinetic impact on the network’s users are fully appreciated beforehand. In pursuit of a kinetically-interpretable centrality score, we discuss the f-score, or frustration score. Each f-score quantifies whether a selected node accelerates or inhibits global mean first passage times to a second, independently-selected target node. We show that this is a natural way of revealing the dynamical importance of a node in some networks. After discussing merits of the f-score metric, we combine spectral and Laplacian matrix theory in order to quickly approximate the exact f-score values, which can otherwise be expensive to compute. Following tests on both synthetic and real medium-sized networks, we report f-score runtime improvements over exact brute force approaches in the range of 0 to 400% with low error (< 3%).

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“…In [60], it has been applied to the problem of triadic closure prediction, producing the best available results so far. Applications to urban traffic modeling can be found in [1,141], while the related notion of communicability angles is able to identify the critical (ie, most diffusive) links in consensus dynamics problems [73]. A notion of spatial efficiency based on the communicability geometry is introduced and used to analyze real-world networks in [68].…”

Section: Communicability Distancementioning

confidence: 99%