The N-intertwined SIS epidemic network model

Mieghem, Piet Van

doi:10.1007/s00607-011-0155-y

Cited by 236 publications

(234 citation statements)

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“…In particular, emerging phenomena of a population of dynamically interacting units has always fascinated scientists. Dynamic phenomena are ubiquitous in nature and play a key role within various contexts in sociology [3], and technology [4]. To date, the problem of how the structural properties of a network influences the convergence and stability of its synchronized states has been extensively investigated and discussed, both numerically and theoretically [5,6,7,8,9], with special attention given to networks of coupled oscillators [10,11,12,13].…”

Section: Introductionmentioning

confidence: 99%

Algebraic connectivity of interdependent networks

Martı́n-Hernández

Wang

Mieghem

et al. 2014

Physica A: Statistical Mechanics and its Applications

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The algebraic connectivity µ N −1 , i.e. the second smallest eigenvalue of the Laplacian matrix, plays a crucial role in dynamic phenomena such as diffusion processes, synchronization stability, and network robustness. In this work we study the algebraic connectivity in the general context of interdependent networks, or network-of-networks (NoN). The present work shows, both analytically and numerically, how the algebraic connectivity of NoNs experiences a transition. The transition is characterized by a saturation of the algebraic connectivity upon the addition of sufficient coupling links (between the two individual networks of a NoN). In practical terms, this shows that NoN topologies require only a fraction of coupling links in order to achieve optimal diffusivity. Furthermore, we observe a footprint of the transition on the properties of Fiedler's spectral bisection.

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Section: Introductionmentioning

confidence: 99%

Algebraic connectivity of interdependent networks

Martı́n-Hernández

Wang

Mieghem

et al. 2014

Physica A: Statistical Mechanics and its Applications

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“…We showed that performance of community detection methods such as spectral bisection and modularity maximization partitioning can be improved by weighting networks with their extremal densities derived from loop modulus. Although, we present some applications of loop modulus, analyzing loop structures on the network can expose different aspects of the network, such as various dynamics on the network, e.g., synchronization and propagation [53][54][55], as well as analyzing complexity of networks [56].…”

Section: Discussionmentioning

confidence: 99%

Network clustering and community detection using modulus of families of loops

et al. 2017

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We study the structure of loops in networks using the notion of modulus of loop families. We introduce an alternate measure of network clustering by quantifying the richness of families of (simple) loops. Modulus tries to minimize the expected overlap among loops by spreading the expected link usage optimally. We propose weighting networks using these expected link usages to improve classical community detection algorithms. We show that the proposed method enhances the performance of certain algorithms, such as spectral partitioning and modularity maximization heuristics, on standard benchmarks.

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“…The analytic tractability, extensions, and several insights on epidemics deduced from the N -intertwined SIS epidemic model are shown in Ref. [13]. In particular, the first-order epidemic threshold equals τ (1) c = 1…”

Section: Susceptible-infected-susceptible Epidemicsmentioning

confidence: 99%