اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدUniversality of eigenvector delocalization and the nature of the SIS phase transition in multiplex networks
120
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Universal spectral properties of multiplex networks allow us to assess the nature of the transition between disease-free and endemic phases in the SIS epidemic spreading model. In a multiplex network, depending on a coupling parameter, $p$, the inverse participation ratio ($IPR$) of the leading eigenvector of the adjacency matrix can be in two different structural regimes: (i) layer-localized and (ii) delocalized. Here we formalize the structural transition point, $p^*$, between these two regimes, showing that there are universal properties regarding both the layer size $n$ and the layer configurations. Namely, we show that $IPR sim n^{-delta}$, with $deltaapprox 1$, and revealed an approximately linear relationship between $p^*$ and the difference between the layers average degrees. Furthermore, we showed that this multiplex structural transition is intrinsically connected with the nature of the SIS phase transition, allowing us to both understand and quantify the phenomenon. As these results are related to the universal properties of the leading eigenvector, we expect that our findings might be relevant to other dynamical processes in complex networks.
قيم البحث
اقرأ أيضاً
Network robustness is a central point in network science, both from a theoretical and a practical point of view. In this paper, we show that layer degradation, understood as the continuous or discrete loss of links weight, triggers a structural trans
ition revealed by an abrupt change in the algebraic connectivity of the graph. Unlike traditional single layer networks, multiplex networks exist in two phases, one in which the system is protected from link failures in some of its layers and one in which all the system senses the failure happening in one single layer. We also give the exact critical value of the weight of the intra-layer links at which the transition occurs for continuous layer degradation and its relation to the value of the coupling between layers. This relation allows us to reveal the connection between the transition observed under layer degradation and the one observed under the variation of the coupling between layers.
Complex networks or graphs provide a powerful framework to understand importance of individuals and their interactions in real-world complex systems. Several graph theoretical measures have been introduced to access importance of the individual in sy
stems represented by networks. Particularly, eigenvector centrality (EC) measure has been very popular due to its ability in measuring importance of the nodes based on not only number of interactions they acquire but also particular structural positions they have in the networks. Furthermore, the presence of certain structural features, such as the existence of high degree nodes in a network is recognized to induce localization transition of the principal eigenvector (PEV) of the networks adjacency matrix. Localization of PEV has been shown to cause difficulties in assigning centrality weights to the nodes based on the EC. We revisit PEV localization and its relation with failure of EC problem, and by using simple model networks demonstrate that in addition to the localization of the PEV, the delocalization of PEV may also create difficulties for using EC as a measure to rank the nodes. Our investigation while providing fundamental insight to the relation between PEV localization and centrality of nodes in networks, suggests that for the networks having delocalized PEVs, it is better to use degree centrality measure to rank the nodes.
Multilayer networks represent multiple types of connections between the same set of nodes. Clearly, a multilayer description of a system adds value only if the multiplex does not merely consist of independent layers, i.e. if the inter-layer overlap i
s nontrivial. On real-world multiplexes, it is expected that the observed overlap may partly result from spurious correlations arising from the heterogeneity of nodes and partly from true interdependencies. However, no rigorous way to disentangle these two effects has been developed. In this paper we introduce an unbiased maximum-entropy model of multiplexes with controllable node degrees and controllable overlap. The model can be mapped to a generalized Ising model where the combination of node heterogeneity and inter-layer coupling leads to the possibility of local phase transitions. In particular, we find that an increased heterogeneity in the network results in different critical points for different pairs of nodes, which in turn leads to local phase transitions that may ultimately increase the overlap. The model allows us to quantify how the overlap can be increased by either increasing the heterogeneity of the network (spurious correlation) or the strength of the inter-layer coupling (true correlation), thereby disentangling the two effects. As an application, we show that the empirical overlap in the International Trade Multiplex is not merely a spurious result of the correlation between node degrees across different layers, but requires a non-zero inter-layer coupling in its modeling.
Many real-world complex systems are best modeled by multiplex networks. The multiplexity has proved to have broad impact on the systems structure and function. Most theoretical studies on multiplex networks to date, however, have largely ignored the
effect of link overlap across layers despite strong empirical evidences for its significance. In this article, we investigate the effect of link overlap in the viability of multiplex networks, both analytically and numerically. Distinctive role of overlapping links in viability and mutual connectivity is emphasized and exploited for setting up proper analytic framework. A rich phase diagram for viability is obtained and greatly diversified patterns of hysteretic behavior in viability are observed in the presence of link overlap. Mutual percolation with link overlap is revisited as a limit of multiplex viability problem, and controversy between existing results is clarified. The distinctive role of overlapping links is further demonstrated by the different responses of networks under random removals of overlapping and non-overlapping links, respectively, as well as under several removal strategies. Our results show that the link overlap strongly facilitates viability and mutual percolation; at the same time, the presence of link overlap poses challenge in analytical approach to the problem.
We develop a theoretical framework for the study of epidemic-like social contagion in large scale social systems. We consider the most general setting in which different communication platforms or categories form multiplex networks. Specifically, we
propose a contact-based information spreading model, and show that the critical point of the multiplex system associated to the active phase is determined by the layer whose contact probability matrix has the largest eigenvalue. The framework is applied to a number of different situations, including a real multiplex system. Finally, we also show that when the system through which information is disseminating is inherently multiplex, working with the graph that results from the aggregation of the different layers is flawed.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
