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Register a new userAnomalous Contagion and Renormalization in Dynamical Networks with Nodal Mobility
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The common real-world feature of individuals migrating through a network -- either in real space or online -- significantly complicates understanding of network processes. Here we show that even though a network may appear static on average, underlying nodal mobility can dramatically distort outbreak profiles. Highly nonlinear dynamical regimes emerge in which increasing mobility either amplifies or suppresses outbreak severity. Predicted profiles mimic recent outbreaks of real-space contagion (social unrest) and online contagion (pro-ISIS support). We show that this nodal mobility can be renormalized in a precise way for a particular class of dynamical networks.
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The metapopulation framework is adopted in a wide array of disciplines to describe systems of well separated yet connected subpopulations. The subgroups or patches are often represented as nodes in a network whose links represent the migration routes among them. The connections have been so far mostly considered as static, but in general evolve in time. Here we address this case by investigating simple contagion processes on time-varying metapopulation networks. We focus on the SIR process and determine analytically the mobility threshold for the onset of an epidemic spreading in the framework of activity-driven network models. We find profound differences from the case of static networks. The threshold is entirely described by the dynamical parameters defining the average number of instantaneously migrating individuals and does not depend on the properties of the static network representation. Remarkably, the diffusion and contagion processes are slower in time-varying graphs than in their aggregated static counterparts, the mobility threshold being even two orders of magnitude larger in the first case. The presented results confirm the importance of considering the time-varying nature of complex networks.
The vast majority of strategies aimed at controlling contagion processes on networks considers the connectivity pattern of the system as either quenched or annealed. However, in the real world many networks are highly dynamical and evolve in time concurrently to the contagion process. Here, we derive an analytical framework for the study of control strategies specifically devised for time-varying networks. We consider the removal/immunization of individual nodes according the their activity in the network and develop a block variable mean-field approach that allows the derivation of the equations describing the evolution of the contagion process concurrently to the network dynamic. We derive the critical immunization threshold and assess the effectiveness of the control strategies. Finally, we validate the theoretical picture by simulating numerically the information spreading process and control strategies in both synthetic networks and a large-scale, real-world mobile telephone call dataset
Complex networks represent the natural backbone to study epidemic processes in populations of interacting individuals. Such a modeling framework, however, is naturally limited to pairwise interactions, making it less suitable to properly describe social contagion, where individuals acquire new norms or ideas after simultaneous exposure to multiple sources of infections. Simplicial contagion has been proposed as an alternative framework where simplices are used to encode group interactions of any order. The presence of higher-order interactions leads to explosive epidemic transitions and bistability which cannot be obtained when only dyadic ties are considered. In particular, critical mass effects can emerge even for infectivity values below the standard pairwise epidemic threshold, where the size of the initial seed of infectious nodes determines whether the system would eventually fall in the endemic or the healthy state. Here we extend simplicial contagion to time-varying networks, where pairwise and higher-order simplices can be created or destroyed over time. By following a microscopic Markov chain approach, we find that the same seed of infectious nodes might or might not lead to an endemic stationary state, depending on the temporal properties of the underlying network structure, and show that persistent temporal interactions anticipate the onset of the endemic state in finite-size systems. We characterize this behavior on higher-order networks with a prescribed temporal correlation between consecutive interactions and on heterogeneous simplicial complexes, showing that temporality again limits the effect of higher-order spreading, but in a less pronounced way than for homogeneous structures. Our work suggests the importance of incorporating temporality, a realistic feature of many real-world systems, into the investigation of dynamical processes beyond pairwise interactions.
Networks are a convenient way to represent complex systems of interacting entities. Many networks contain communities of nodes that are more densely connected to each other than to nodes in the rest of the network. In this paper, we investigate the detection of communities in temporal networks represented as multilayer networks. As a focal example, we study time-dependent financial-asset correlation networks. We first argue that the use of the modularity quality function---which is defined by comparing edge weights in an observed network to expected edge weights in a null network---is application-dependent. We differentiate between null networks and null models in our discussion of modularity maximization, and we highlight that the same null network can correspond to different null models. We then investigate a multilayer modularity-maximization problem to identify communities in temporal networks. Our multilayer analysis only depends on the form of the maximization problem and not on the specific quality function that one chooses. We introduce a diagnostic to measure emph{persistence} of community structure in a multilayer network partition. We prove several results that describe how the multilayer maximization problem measures a trade-off between static community structure within layers and larger values of persistence across layers. We also discuss some computational issues that the popular Louvain heuristic faces with temporal multilayer networks and suggest ways to mitigate them.
In this work, we investigate a heterogeneous population in the modified Hegselmann-Krause opinion model on complex networks. We introduce the Shannon information entropy about all relative opinion clusters to characterize the cluster profile in the final configuration. Independent of network structures, there exists the optimal stubbornness of one subpopulation for the largest number of clusters and the highest entropy. Besides, there is the optimal bounded confidence (or subpopulation ratio) of one subpopulation for the smallest number of clusters and the lowest entropy. However, network structures affect cluster profiles indeed. A large average degree favors consensus for making different networks more similar with complete graphs. The network size has limited impact on cluster profiles of heterogeneous populations on scale-free networks but has significant effects upon those on small-world networks.
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