Inter-layer Degree Correlations Research Articles

Coupled Information-Epidemic Spreading Dynamics with Selective Mass Media.

As a pandemic emerges, information on epidemic prevention disseminates among the populace, and the propagation of that information interacts with the proliferation of the disease. Mass media serve a pivotal function in facilitating the dissemination of epidemic-related information. Investigating coupled information-epidemic dynamics, while accounting for the promotional effect of mass media in information dissemination, is of significant practical relevance. Nonetheless, in the extant research, scholars predominantly employ an assumption that mass media broadcast to all individuals equally within the network: this assumption overlooks the practical constraint imposed by the substantial social resources required to accomplish such comprehensive promotion. In response, this study introduces a coupled information-epidemic spreading model with mass media that can selectively target and disseminate information to a specific proportion of high-degree nodes. We employed a microscopic Markov chain methodology to scrutinize our model, and we examined the influence of the various model parameters on the dynamic process. The findings of this study reveal that mass media broadcasts directed towards high-degree nodes within the information spreading layer can substantially reduce the infection density of the epidemic, and raise the spreading threshold of the epidemic. Additionally, as the mass media broadcast proportion increases, the suppression effect on the disease becomes stronger. Moreover, with a constant broadcast proportion, the suppression effect of mass media promotion on epidemic spreading within the model is more pronounced in a multiplex network with a negative interlayer degree correlation, compared to scenarios with positive or absent interlayer degree correlation.

Dynamics of corruption on correlated multiplex networks with overlap

To get further insight into the mechanism behind driving the social behaviors for a compartmental flow model of corruption on multiplex networks, we apply the model to the duplex networks, where different flows among three states (Honest, Corrupt, Ostracism) take place separately on a particular layer. In our work, we aim to unravel the impact of edge overlap and interlayer degree correlations on the evolution of corruption by considering different underlying contact networks. To assess the role of the edge overlap (m) on the diffusion of corruption, we produce various values of m by rewiring the edges of one of two synthetic networks. In addition, to explore the significance of interlayer degree correlations, we generate the duplex networks with specific degree correlated patterns giving rise to different values of m. The results show that the influence of the structural properties becomes gradually prominent as the corruption and delation rate decrease. The smaller m produced by rewiring the biased edges makes the extension of the stability region of full honesty state though not clearly noticeable. However, the larger m determined by the degree correlation patterns is prone to the presence of the stability region of the full H state. The findings reveal that edge overlap caused by rewiring links barely has an effect on the evolution regardless of duplex networks being uncorrelated or correlated. Nevertheless, the interlayer correlated coupling plays a major role in the stationary states of the corruption dynamics.

Effects of the information-driven awareness on epidemic spreading on multiplex networks.

In this study, we examine the impact of information-driven awareness on the spread of an epidemic from the perspective of resource allocation by comprehensively considering a series of realistic scenarios. A coupled awareness-resource-epidemic model on top of multiplex networks is proposed, and a Microscopic Markov Chain Approach is adopted to study the complex interplay among the processes. Through theoretical analysis, the infection density of the epidemic is predicted precisely, and an approximate epidemic threshold is derived. Combining both numerical calculations and extensive Monte Carlo simulations, the following conclusions are obtained. First, during a pandemic, the more active the resource support between individuals, the more effectively the disease can be controlled; that is, there is a smaller infection density and a larger epidemic threshold. Second, the disease can be better suppressed when individuals with small degrees are preferentially protected. In addition, there is a critical parameter of contact preference at which the effectiveness of disease control is the worst. Third, the inter-layer degree correlation has a "double-edged sword" effect on spreading dynamics. In other words, when there is a relatively lower infection rate, the epidemic threshold can be raised by increasing the positive correlation. By contrast, the infection density can be reduced by increasing the negative correlation. Finally, the infection density decreases when raising the relative weight of the global information, which indicates that global information about the epidemic state is more efficient for disease control than local information.

Cascading failures in multiplex network under flow redistribution

Understanding the robustness of real-world complex systems is a key step to design reliable systems and maintain their stability and normal functions. In this paper, we propose a flow redistribution model in two-layer multiplex network and study its cascading dynamics, where an initial edge failure may cause large cascading failure through the network. In our model, initially an edge on layer A fails and a proportion a of flow on the edge is redistributed to the overlap link in layer B if there exists one, while the remaining (1−a) proportion of flow is redistributed under a local weighted flow redistribution rule. Similarly a proportion b of flow of a failed edge in layer B is redistributed to the overlap link in layer A. The cascading failure continues until a steady state is reached. We analytically calculate the resilience threshold of the network and validate it by numerical simulations. We firstly find that there is an optimal weighting of edge flow at which the robustness of the system is the highest. Then we find that for the two coupled layers of networks with obviously different resilience, the layer with smaller resilience benefits from the coupled system while the robustness of the layer with larger resilience is damaged due to inter-layer cascading process. The coupled system is the most robust when the inter-layer degree correlation is maximally positive.

An efficient layer node attack strategy to dismantle large multiplex networks

Network dismantling aims to identify the minimum set of nodes whose removal breaks the network into components of sub-extensive size. The solution to this problem is significant for designing optimal strategies for immunization policies, information spreading, and network attack. Modern systems, such as social networks and critical infrastructure networks, which consist of nodes connected by links of multiple types can be encapsulated into the framework of multiplex networks. Here we focus on the dismantling problem in multiplex networks under layer node-based attack, and propose an efficient dismantling algorithm based on network decycling. Experiments on synthetic and real-world networks show that the proposed algorithm outperforms existing algorithms by a considerable margin. We also show how the robustness of a multiplex network is affected by the interlayer degree correlation. Our results shed light on the design of more resilient network systems and the effective destruction of harmful networks.

Optimal percolation in correlated multilayer networks with overlap

Multilayer networks have been found to be prone to abrupt cascading failures under random and targeted attacks, but most of the targeting algorithms proposed so far have been mainly tested on uncorrelated systems. Here we show that the size of the critical percolation set of a multilayer network is substantially affected by the presence of inter-layer degree correlations and edge overlap. We provide extensive numerical evidence which confirms that the state-of-the-art optimal percolation strategies consistently fail to identify minimal percolation sets in synthetic and real-world correlated multilayer networks, thus overestimating their robustness. We propose two new targeting algorithms, based on the local estimation of path disruptions away from a given node, and a family of Pareto-efficient strategies that take into account both intra-layer and inter-layer heuristics, and can be easily extended to multiplex networks with an arbitrary number of layers. We show that these strategies consistently outperform existing attacking algorithms, on both synthetic and real-world multiplex networks, and provide some interesting insights about the interplay of correlations and overlap in determining the hyperfragility of real-world multilayer networks. Overall, the results presented in the paper suggest that we are still far from having fully identified the salient ingredients determining the robustness of multiplex networks to targeted attacks.

Generalized k-core percolation on correlated and uncorrelated multiplex networks.

It has been recognized that multiplexes and interlayer degree correlations can play a crucial role in the resilience of many real-world complex systems. Here we introduce a multiplex pruning process that removes nodes of degree less than k_{i} and their nearest neighbors in layer i for i=1,...,m, and establish a generic framework of generalized k-core (Gk-core) percolation over interlayer uncorrelated and correlated multiplex networks of m layers, where k=(k_{1},...,k_{m}) and m is the total number of layers. Gk-core exhibits a discontinuous phase transition for all k owing to cascading failures. We have unraveled the existence of a tipping point of the number of layers, above which the Gk-core collapses abruptly. This dismantling effect of multiplexity on Gk-core percolation shows a diminishing marginal utility in homogeneous networks when the number of layers increases. Moreover, we have found the assortative mixing for interlayer degrees strengthens the Gk-core but still gives rise to discontinuous phase transitions as compared to the uncorrelated counterparts. Interlayer disassortativity on the other hand weakens the Gk-core structure. The impact of correlation effect on Gk-core tends to be more salient systematically over k for heterogenous networks than homogeneous ones.

Containing rumors spreading on correlated multiplex networks

Rumors flooding on rapidly-growing online social networks have geared much attention from many fronts. Individuals can transmit rumors via numerous channels since they can be active on multiple platforms. However, no systematic theoretical research of rumors containing dynamics on multiplex networks has been conducted yet. In this study, we propose a family of containing strategies based on the degree product of each user on the multiplex networks. Then, we develop a heterogeneous edge-based compartmental theory to comprehend the containing dynamics. The simulation results demonstrate that strategies with preference to block users with large can significantly reduce the rumor outbreak size and enlarge the threshold. Besides, better performance can be expected on heterogeneous multiplex networks with the increasing of preference intensity and degree heterogeneity. Moreover, take the inter-layer degree correlations rs into consideration, the strategy performs best on multiplex networks with rs = −1, rs = 1 the second, and rs = 0 the last. On the contrary, if we prefer to block users with small rather than large , the containing performance will be worse than that of blocking users randomly on most multiplex networks except for uncorrelated multiplex networks with uniform degree distribution. We found that the blocking preferences have no influence on the containing results on uncorrelated multiplex networks with uniform degree distribution. Our theoretical analysis can well predict the rumors containing results and performance differences in all the cases studied. The systematic theoretical research of rumors containing dynamics on multiplex networks in this study will offer inspirations for further investigations on this issue.

Percolation on branching simplicial and cell complexes and its relation to interdependent percolation.

Network geometry has strong effects on network dynamics. In particular, the underlying hyperbolic geometry of discrete manifolds has recently been shown to affect their critical percolation properties. Here we investigate the properties of link percolation in nonamenable two-dimensional branching simplicial and cell complexes, i.e., simplicial and cell complexes in which the boundary scales like the volume. We establish the relation between the equations determining the percolation probability in random branching cell complexes and the equation for interdependent percolation in multiplex networks with interlayer degree correlation equal to one. By using this relation we show that branching cell complexes can display more than two percolation phase transitions: the upper percolation transition, the lower percolation transition, and one or more intermediate phase transitions. At these additional transitions the percolation probability and the fractal exponent both feature a discontinuity. Furthermore, by using the renormalization group theory we show that the upper percolation transition can belong to various universality classes including the Berezinskii-Kosterlitz-Thouless (BKT) transition, the discontinuous percolation transition, and continuous transitions with anomalous singular behavior that generalize the BKT transition.

Cascading failures on correlated interdependent networks with dependency groups

The topologies of interdependent networks markedly affect the cascading failures and phase transition. However, the effects of interlayer degree correlations on cascading failures on interdependent networks with dependency groups have not been investigated. In this paper, we propose a cascading failure model on correlated interdependent networks with dependency groups, and use a percolation theory to describe the final state of the dynamics. Through extensive numerical simulations and theoretical analysis, we find that interlayer degree correlations enhance the robustness of the system. On networks with homogeneous degree distribution, the system always exhibits a discontinuous phase transition. However, on networks with heterogeneous degree distributions, the phase transition is continuous (discontinuous) for strong (weak) interlayer degree correlations. The theoretical and numerical predictions agree well with each other.

Cascading failures in scale-free interdependent networks.

Large cascades are a common occurrence in many natural and engineered complex systems. In this paper we explore the propagation of cascades across networks using realistic network topologies, such as heterogeneous degree distributions, as well as intra- and interlayer degree correlations. We find that three properties, scale-free degree distribution, internal network assortativity, and cross-network hub-to-hub connections, are all necessary components to significantly reduce the size of large cascades in the Bak-Tang-Wiesenfeld sandpile model. We demonstrate that correlations present in the structure of the multilayer network influence the dynamical cascading process and can prevent failures from spreading across connected layers. These findings highlight the importance of internal and cross-network topology in optimizing robustness of interconnected systems.

Social contagions on correlated multiplex networks

The existence of interlayer degree correlations has been disclosed by abundant multiplex network analysis. However, how they impose on the dynamics of social contagions are remain largely unknown. In this paper, we propose a non-Markovian social contagion model in multiplex networks with inter-layer degree correlations to delineate the behavior spreading, and develop an edge-based compartmental (EBC) theory to describe the model. We find that multiplex networks promote the final behavior adoption size. Remarkably, it can be observed that the growth pattern of the final behavior adoption size, versus the behavioral information transmission probability, changes from discontinuous to continuous once decreasing the behavior adoption threshold in one layer. We finally unravel that the inter-layer degree correlations play a role on the final behavior adoption size but have no effects on the growth pattern, which is coincidence with our prediction by using the suggested theory.

Out-of-hospital cardiac arrest of cardiac etiology increases in the elderly population

Many recent studies have demonstrated that individual awareness of disease may significantly affect the spreading process of infectious disease. In the majority of these studies, the response of the awareness is generally treated homogeneously. Considering of diversity and heterogeneity in the human behavior which widely exist under different circumstances, in this paper we study heterogeneous response when people are aware of the prevalence of infectious diseases. Specifically, we consider that an individual with more neighbors may take more preventive measures as a reaction when he is aware of the disease. A suppression strength is introduced to describe such heterogeneity, and we find that a more evident heterogeneity may cause a more effective suppressing effect to the spreading of epidemics. A mean-field theory is developed to support the results which are verified on the multiplex networks with different interlayer degree correlation.

Geometric Correlations Mitigate the Extreme Vulnerability of Multiplex Networks against Targeted Attacks

We show that real multiplex networks are unexpectedly robust against targeted attacks on high-degree nodes and that hidden interlayer geometric correlations predict this robustness. Without geometric correlations, multiplexes exhibit an abrupt breakdown of mutual connectivity, even with interlayer degree correlations. With geometric correlations, we instead observe a multistep cascading process leading into a continuous transition, which apparently becomes fully continuous in the thermodynamic limit. Our results are important for the design of efficient protection strategies and of robust interacting networks in many domains.

The impact of heterogeneous response on coupled spreading dynamics in multiplex networks

Many recent studies have demonstrated that individual awareness of disease may significantly affect the spreading process of infectious disease. In the majority of these studies, the response of the awareness is generally treated homogeneously. Considering of diversity and heterogeneity in the human behavior which widely exist under different circumstances, in this paper we study heterogeneous response when people are aware of the prevalence of infectious diseases. Specifically, we consider that an individual with more neighbors may take more preventive measures as a reaction when he is aware of the disease. A suppression strength is introduced to describe such heterogeneity, and we find that a more evident heterogeneity may cause a more effective suppressing effect to the spreading of epidemics. A mean-field theory is developed to support the results which are verified on the multiplex networks with different interlayer degree correlation.

Efficient exploration of multiplex networks

Efficient techniques to navigate networks with local information are fundamental to sample large-scale online social systems and to retrieve resources in peer-to-peer systems. Biased random walks, i.e. walks whose motion is biased on properties of neighbouring nodes, have been largely exploited to design smart local strategies to explore a network, for instance by constructing maximally mixing trajectories or by allowing an almost uniform sampling of the nodes. Here we introduce and study biased random walks on multiplex networks, graphs where the nodes are related through different types of links organised in distinct and interacting layers, and we provide analytical solutions for their long-time properties, including the stationary occupation probability distribution and the entropy rate. We focus on degree-biased random walks and distinguish between two classes of walks, namely those whose transition probability depends on a number of parameters which is extensive in the number of layers, and those whose motion depends on intrinsically multiplex properties of the neighbouring nodes. We analyse the effect of the structure of the multiplex network on the steady-state behaviour of the walkers, and we find that heterogeneous degree distributions as well as the presence of inter-layer degree correlations and edge overlap determine the extent to which a multiplex can be efficiently explored by a biased walk. Finally we show that, in real-world multiplex transportation networks, the trade-off between efficient navigation and resilience to link failure has resulted into systems whose diffusion properties are qualitatively different from those of appropriately randomised multiplex graphs. This fact suggests that multiplexity is an important ingredient to include in the modelling of real-world systems.

Escaping the avalanche collapse in self-similar multiplexes

We deduce and discuss the implications of self-similarity for the robustness to failure of multiplexes, depending on interlayer degree correlations. First, we define self-similarity of multiplexes and we illustrate the concept in practice using the configuration model ensemble. Circumscribing robustness to survival of the mutually percolated state, we find a new explanation based on self-similarity both for the observed fragility of interconnected systems of networks and for their robustness to failure when interlayer degree correlations are present. Extending the self-similarity arguments, we show that interlayer degree correlations can change completely the global connectivity properties of self-similar multiplexes, so that they can even recover a zero percolation threshold and a continuous transition in the thermodynamic limit, qualitatively exhibiting thus the ordinary percolation properties of noninteracting networks. We confirm these results with numerical simulations.

Network robustness of multiplex networks with interlayer degree correlations

We study the robustness properties of multiplex networks consisting of multiple layers of distinct types of links, focusing on the role of correlations between degrees of a node in different layers. We use generating function formalism to address various notions of the network robustness relevant to multiplex networks, such as the resilience of ordinary and mutual connectivity under random or targeted node removals, as well as the biconnectivity. We found that correlated coupling can affect the structural robustness of multiplex networks in diverse fashion. For example, for maximally correlated duplex networks, all pairs of nodes in the giant component are connected via at least two independent paths and network structure is highly resilient to random failure. In contrast, anticorrelated duplex networks are on one hand robust against targeted attack on high-degree nodes, but on the other hand they can be vulnerable to random failure.