Epidemic spreading in modular time-varying networks

Nadini, Matthieu; Sun, Kaiyuan; Ubaldi, Enrico; Starnini, Michele; Rizzo, Alessandro; Perra, Nicola

doi:10.1038/s41598-018-20908-x

Cited by 95 publications

(93 citation statements)

References 93 publications

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“…[11] showed leveraging a heterogeneous network among people to yield more resistance against the epidemic spread of the virus. Epidemic spreading is an important issue that was considered in other networks likes time-varying networks [42] and adaptive ones [43]. Nadini et al [42] used SIR and SIS models and investigated effects of modular and temporal connectivity patterns on epidemic spreading.…”

Section: Topic Diffusionmentioning

confidence: 99%

Deep learning approach on information diffusion in heterogeneous networks

Molaei

Zare

Veisi

2020

Knowledge-Based Systems

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There are many real-world complex systems with multi-type interacting entities that can be regarded as heterogeneous networks including human connections and biological evolutions. One of the main issues in such networks is to predict information diffusion such as shape, growth and size of social events and evolutions in the future. While there exist a variety of works on this topic mainly using a threshold-based approach, they suffer from the local viewpoint on the network and sensitivity to the threshold parameters. In this paper, information diffusion is considered through a latent representation learning of the heterogeneous networks to encode in a deep learning model. To this end, we propose a novel meta-path representation learning approach, Heterogeneous Deep Diffusion(HDD), to exploit meta-paths as main entities in networks. At first, the functional heterogeneous structures of the network are learned by a continuous latent representation through traversing meta-paths with the aim of global end-to-end viewpoint. Then, the wellknown deep learning architectures are employed on our generated features to predict diffusion processes in the network. The proposed approach enables us to apply it on different information diffusion tasks such as topic diffusion and cascade prediction. We demonstrate the proposed approach on benchmark network datasets through the well-known evaluation measures. The experimental results show that our approach outperforms the earlier state-of-the-art methods.

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Section: Topic Diffusionmentioning

confidence: 99%

Deep learning approach on information diffusion in heterogeneous networks

Molaei

Zare

Veisi

2020

Knowledge-Based Systems

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“…The mathematical analysis above suggests that the ETFM error is minimized, while the error of the EADM should decay as the inverse of the size of the network, 1/N, and coincide with predictions from equation (23). The numerical relative error and normalized root mean squared error are computed as follows:…”

Section: Numericsmentioning

confidence: 99%

“…Comparison between the theoretical relative error (RE) and normalized root mean squared error (NRMSE) of the EADM, in equation(23), with numerical results of both the EADM and ETFM, in equation(24). Homogeneous backbone networks with λ = 0.02 are studied in panels (a) and (d); homogeneous backbone networks with λ = 0.7 are examined in panels (b) and (e); and of heterogeneous backbone networks with λ min = 0.02 are considered in panels (c) and (f).…”

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confidence: 99%

Reconstructing irreducible links in temporal networks: which tool to choose depends on the network size

2020

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Filtering information in complex networks entails the process of removing interactions explained by a proper null hypothesis and retaining the remaining interactions, which form the backbone network. The reconstructed backbone network depends upon the accuracy and reliability of the available tools, which, in turn, are affected by the specific features of the available dataset. Here, we examine the performance of three approaches for the discovery of backbone networks, in the presence of heterogeneous, time-varying node properties. In addition to the recently proposed evolving activity driven model, we extend two existing approaches (the disparity filter and the temporal fitness model) to tackle time-varying phenomena. Our analysis focuses on the influence of the network size, which was previously shown to be a determining factor for the performance of the evolving activity driven model. Through mathematical and numerical analysis, we propose general guidelines for the use of these three approaches based on the available dataset. For small networks, the evolving temporal fitness model offers a more reasonable trade-off between the number of links assigned to the backbone network and the accuracy of their inference. The main limitation of this methodology lies in its computational cost, which becomes excessively high for large networks. In this case, the evolving activity driven model could be a valid substitute to the evolving temporal fitness model. If one seeks to minimize the number of links inaccurately included in the backbone network at the risk of dismissing many links that could belong to it, then the temporal disparity filter would be the approach-of-choice. Overall, our contribution expands the toolbox of network discovery in the technical literature and should help users in choosing the right network discovery instrument, depending on the problem considered.

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Section: Introductionmentioning

confidence: 99%

“…the constant rate at which an agent sends links to other peers, following a Poissonian process. The memoryless property implied by the Markovian dynamics greatly simplifies the mathematical treatment of these models, regarding both the topological properties of the time-integrated network representation [7], and the description of the dynamical processes unfolding on activity-driven networks [8][9][10][11][12][13].However, the Markovian assumption in temporal network modeling has been challenged by the increasing availability of time-resolved data on different kinds of interactions, ranging from phone communications [14] and face-to-face interactions [15], to natural phenomena [16,17], biological processes [18] and physiological systems [19][20][21]. These empirical observations have uncovered a rich variety of dynamical properties, in particular that the inter-event times t between two successive interactions (either the creation of the same edge or two consecutive creations of an edge by the same node), ψ(t), follows heavy-tailed distributions [15,22,23].…”

mentioning

confidence: 99%

Random walks in non-Poissoinan activity driven temporal networks

2019

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The interest in non-Markovian dynamics within the complex systems community has recently blossomed, due to a new wealth of time-resolved data pointing out the bursty dynamics of many natural and human interactions, manifested in an inter-event time between consecutive interactions showing a heavy-tailed distribution. In particular, empirical data has shown that the bursty dynamics of temporal networks can have deep consequences on the behavior of the dynamical processes running on top of them. Here, we study the case of random walks, as a paradigm of diffusive processes, unfolding on temporal networks generated by a non-Poissonian activity driven dynamics. We derive analytic expressions for the steady state occupation probability and first passage time distribution in the infinite network size and strong aging limits, showing that the random walk dynamics on non-Markovian networks are fundamentally different from what is observed in Markovian networks. We found a particularly surprising behavior in the limit of diverging average inter-event time, in which the random walker feels the network as homogeneous, even though the activation probability of nodes is heterogeneously distributed. Our results are supported by extensive numerical simulations. We anticipate that our findings may be of interest among the researchers studying non-Markovian dynamics on time-evolving complex topologies. IntroductionTemporal networks [1, 2] constitute a recent new description of complex systems, that, moving apart from the classical static paradigm of network science [3], in which nodes and edges do not change in time, consider dynamic connections that can be created, destroyed or rewired at different time scales. Within this framework, a first round of studies proposed temporal network models ruled by homogeneous Markovian dynamics [4]. A prominent example is represented by the activity-driven model [5] (see also [6]), in which nodes are characterized by a different degree of activity, i.e. the constant rate at which an agent sends links to other peers, following a Poissonian process. The memoryless property implied by the Markovian dynamics greatly simplifies the mathematical treatment of these models, regarding both the topological properties of the time-integrated network representation [7], and the description of the dynamical processes unfolding on activity-driven networks [8][9][10][11][12][13].However, the Markovian assumption in temporal network modeling has been challenged by the increasing availability of time-resolved data on different kinds of interactions, ranging from phone communications [14] and face-to-face interactions [15], to natural phenomena [16,17], biological processes [18] and physiological systems [19][20][21]. These empirical observations have uncovered a rich variety of dynamical properties, in particular that the inter-event times t between two successive interactions (either the creation of the same edge or two consecutive creations of an edge by the same node), ψ(t), follows heavy-tailed distributions...

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Epidemic spreading in modular time-varying networks

Cited by 95 publications

References 93 publications

Deep learning approach on information diffusion in heterogeneous networks

Deep learning approach on information diffusion in heterogeneous networks

Reconstructing irreducible links in temporal networks: which tool to choose depends on the network size

Random walks in non-Poissoinan activity driven temporal networks

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