The problem of finding optimal set of users for influencing others in the social network has been widely studied. Because it is NP-hard, some heuristics were proposed to find sub-optimal solutions. Still, one of the commonly used assumption is the one that seeds are chosen on the static network, not the dynamic one. This static approach is in fact far from the real-world networks, where new nodes may appear and old ones dynamically disappear in course of time.
Having these conclusions in mind, it was decided to evaluate how the most typical heuristics based on the network structure perform on temporal and static networks. A special attention has been turned to observation of dynamics of the influence that spreads over temporal (changing) network after choosing initial seed sets. Indeed, this direction is emerging, because first work studying spreading phenomenon in temporal networks is published nowadays @cite_20 @cite_34 . However, the authors did not focus on seeding strategies there, but they analysed the process under different assumptions for the aggregation level.
@cite_34 @cite_20
2579376689 2048186046 2962802798 1977878271
Many studies in the field of information spread through social networks focus on the detection of influencers. The spread dynamics in most of these studies assumes these influencers are first selected and "infected" with a message, and then this message spreads through the networks by a viral process. The following work presents some difficulties with this separation between the infection stage and the viral stage, and provides a case where an increased effort spent on the spread of an idea results in lower final rates of spread. Such results can be prevented by the Scheduling Seeding approach. This approach gradually plans the timing of infection for each particular node as the viral process progresses. It outperforms the initial seeding approach, and prevents the occurrence of the counter-intuitive (and unwanted) results where a greater effort results in a less successful spread. A simple but effective heuristics to detect what node to seed and where is provided. The time variation of contacts in a networked system may fundamentally alter the properties of spreading processes and affect the condition for large-scale propagation, as encoded in the epidemic threshold. Despite the great interest in the problem for the physics, applied mathematics, computer science, and epidemiology communities, a full theoretical understanding is still missing and currently limited to the cases where the timescale separation holds between spreading and network dynamics or to specific temporal network models. We consider a Markov chain description of the susceptible-infectious-susceptible process on an arbitrary temporal network. By adopting a multilayer perspective, we develop a general analytical derivation of the epidemic threshold in terms of the spectral radius of a matrix that encodes both network structure and disease dynamics. The accuracy of the approach is confirmed on a set of temporal models and empirical networks and against numerical results. In addition, we explore how the threshold changes when varying the overall time of observation of the temporal network, so as to provide insights on the optimal time window for data collection of empirical temporal networked systems. Our framework is of both fundamental and practical interest, as it offers novel understanding of the interplay between temporal networks and spreading dynamics. Can evolving networks be inferred and modeled without directly observing their nodes and edges? In many applications, the edges of a dynamic network might not be observed, but one can observe the dynamics of stochastic cascading processes (e.g., information diffusion, virus propagation) occurring over the unobserved network. While there have been efforts to infer networks based on such data, providing a generative probabilistic model that is able to identify the underlying time-varying network remains an open question. Here we consider the problem of inferring generative dynamic network models based on network cascade diffusion data. We propose a novel framework for providing a non-parametric dynamic network model---based on a mixture of coupled hierarchical Dirichlet processes---based on data capturing cascade node infection times. Our approach allows us to infer the evolving community structure in networks and to obtain an explicit predictive distribution over the edges of the underlying network---including those that were not involved in transmission of any cascade, or are likely to appear in the future. We show the effectiveness of our approach using extensive experiments on synthetic as well as real-world networks. We introduce a general stochastic model for the spread of rumours, and derive mean-field equations that describe the dynamics of the model on complex social networks (in particular, those mediated by the Internet). We use analytical and numerical solutions of these equations to examine the threshold behaviour and dynamics of the model on several models of such networks: random graphs, uncorrelated scale-free networks and scale-free networks with assortative degree correlations. We show that in both homogeneous networks and random graphs the model exhibits a critical threshold in the rumour spreading rate below which a rumour cannot propagate in the system. In the case of scale-free networks, on the other hand, this threshold becomes vanishingly small in the limit of infinite system size. We find that the initial rate at which a rumour spreads is much higher in scale-free networks than in random graphs, and that the rate at which the spreading proceeds on scale-free networks is further increased when assortative degree correlations are introduced. The impact of degree correlations on the final fraction of nodes that ever hears a rumour, however, depends on the interplay between network topology and the rumour spreading rate. Our results show that scale-free social networks are prone to the spreading of rumours, just as they are to the spreading of infections. They are relevant to the spreading dynamics of chain emails, viral advertising and large-scale information dissemination algorithms on the Internet.