2021
DOI: 10.1088/2632-072x/abdd98
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Dissecting localization phenomena of dynamical processes on networks

Abstract: Localization phenomena permeate many branches of physics playing a fundamental role on dynamical processes evolving on heterogeneous networks. These localization analyses are frequently grounded, for example, on eigenvectors of adjacency or non-backtracking matrices which emerge in theories of dynamic processes near to an active to inactive phase transition. We advance in this problem gauging nodal activity to quantify the localization in dynamical processes on networks whether they are near to a transition or… Show more

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Cited by 8 publications
(9 citation statements)
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“…The empirical spectral density of the adjacency matrix and the localization of its eigenvectors are important to understand algorithms for node centrality [2,3] and community detection [4,5], as well as the interplay between the structure of networks and dynamical processes on them. In fact, the leading eigenpair of the adjacency matrix governs the spreading of diseases [6,7], the synchronization transition [8,9], and the linear stability of large complex systems [10][11][12][13]. In condensed matter physics, models defined on random graphs represent mean-field versions of finite-dimensional lattices which mimic the effects of finite coordination number.…”
Section: Introductionmentioning
confidence: 99%
“…The empirical spectral density of the adjacency matrix and the localization of its eigenvectors are important to understand algorithms for node centrality [2,3] and community detection [4,5], as well as the interplay between the structure of networks and dynamical processes on them. In fact, the leading eigenpair of the adjacency matrix governs the spreading of diseases [6,7], the synchronization transition [8,9], and the linear stability of large complex systems [10][11][12][13]. In condensed matter physics, models defined on random graphs represent mean-field versions of finite-dimensional lattices which mimic the effects of finite coordination number.…”
Section: Introductionmentioning
confidence: 99%
“…We have so far thoroughly described epidemic detriment due to spatial homogenization of populations caused by recurrent mobility. [61,88] This mechanism can be suited more generically as the delocalization process of the epidemic activity, [89] revised with some examples in this section. Localization phenomena driven by disordered inhomogeneities play a central role on condensed matter physics and can change drastically the The population asymmetry is modulated by 𝛼 for all cases.…”
Section: Epidemic Detriment As Delocalization Processes On Complex Ne...mentioning
confidence: 99%
“…There are different methods to avoid the absorbing configurations such as the SQS method [28] (section II A), which constrains the sampling to active configurations, and the RBC [24] (section II B), in which the system returns to the pre-absorbing configuration when absorbing one is visited. In the case of complex networks, which are highly heterogeneous, the localization on subextensive regions imposes further difficulties in the analysis of QS states [15,19]. While, on the one hand, the SQS is most general and able to capture localized phases of epidemics on networks [15,16,30], it has high computational and algorithmic complexity.…”
Section: Conclusion and Prospectsmentioning
confidence: 99%
“…The RAT method was applied to the SIS model on a variety of complex networks, which are characterized by strong localization effects [15,16,19] and compared with the RBC and SQS methods. We report that all methods provide the same epidemic threshold on multiplex and uncorrelated scale-free networks (degree exponent γ < 3) but the finite-size scaling of the critical epidemic prevalence (density of active vertices at the threshold) of RBC differs of both SQS and RAT that match each other.…”
Section: Conclusion and Prospectsmentioning
confidence: 99%
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