Imperfect spreading on temporal networks

We study spreading on networks where the contact dynamics between the nodes is governed by a random process and where the inter-contact time distribution may differ from the exponential. We consider a process of imperfect spreading, where transmission is successful with a determined probability at each contact. We first derive an expression for the inter-success time distribution, determining the speed of the propagation, and then focus on a problem related to epidemic spreading, by estimating the epidemic threshold in a system where nodes remain infectious during a finite, random period of time. Finally, we discuss the implications of our work to design an efficient strategy to enhance spreading on temporal networks.Comment: 5 page

Random walk on temporal networks with lasting edges

We consider random walks on dynamical networks where edges appear and disappear during finite time intervals. The process is grounded on three independent stochastic processes determining the walker's waiting-time, the up-time and down-time of edges activation. We first propose a comprehensive analytical and numerical treatment on directed acyclic graphs. Once cycles are allowed in the network, non-Markovian trajectories may emerge, remarkably even if the walker and the evolution of the network edges are governed by memoryless Poisson processes. We then introduce a general analytical framework to characterize such non-Markovian walks and validate our findings with numerical simulations.Comment: 18 pages, 18 figure

Backtracking and mixing rate of diffusion on uncorrelated temporal networks

We consider the problem of diffusion on temporal networks, where the dynamics of each edge is modelled by an independent renewal process. Despite the apparent simplicity of the model, the trajectories of a random walker exhibit non-trivial properties. Here, we quantify the walker’s tendency to backtrack at each step (return where he/she comes from), as well as the resulting effect on the mixing rate of the process. As we show through empirical data, non-Poisson dynamics may significantly slow down diffusion due to backtracking, by a mechanism intrinsically different from the standard bus paradox and related temporal mechanisms. We conclude by discussing the implications of our work for the interpretation of results generated by null models of temporal networks

Rock–paper–scissors dynamics from random walks on temporal multiplex networks

Abstract We study diffusion on a multiplex network where the contact dynamics between the nodes is governed by a random process and where the waiting-time distribution differs for edges from different layers. We study the impact on a random walk of the competition that naturally emerges between the edges of the different layers. In opposition to previous studies, which have imposed a priori inter-layer competition, the competition is here induced by the heterogeneity of the activity on the different layers. We first study the precedence relation between different edges and by extension between different layers, and show that it determines biased paths for the walker. We also discuss the emergence of cyclic, rock–paper–scissors effects on random walks, when the precedence between layers is non-transitive. Finally, we numerically show the slowing-down effect due to the competition on a multiplex network with heterogeneous layers activity as the walker is likely to be trapped for a longer time either on a single layer, or on an oriented cycle

Rock–paper–scissors dynamics from random walks on temporal multiplex networks

We study diffusion on a multiplex network where the contact dynamics between the nodes is governed by a random process and where the waiting-time distribution differs for edges from different layers. We study the impact on a random walk of the competition that naturally emerges between the edges of the different layers. In opposition to previous studies, which have imposed a priori inter-layer competition, the competition is here induced by the heterogeneity of the activity on the different layers. We first study the precedence relation between different edges and by extension between different layers, and show that it determines biased paths for the walker. We also discuss the emergence of cyclic, rock–paper–scissors effects on random walks, when the precedence between layers is non-transitive. Finally, we numerically show the slowing-down effect due to the competition on a multiplex network with heterogeneous layers activity as the walker is likely to be trapped for a longer time either on a single layer, or on an oriented cycle

Temporal Sequence of Retweets Help to Detect Influential Nodes in Social Networks

Identification of influential users in online social networks allows to facilitate efficient information diffusion to a large part of the network, thus benefiting diverse applications including viral marketing, disease control and news dissemination. Existing methods have mainly relied on the network structure only for the detection of influential users. In this paper, we enrich this approach by proposing a fast, efficient and unsupervised algorithm SmartInf to detect a set of influential users by identifying anchor nodes from temporal sequence of retweets in Twitter cascades. Such anchor nodes provide important signatures of tweet diffusion across multiple diffusion localities and hence act as precursors for detection of influential nodes1 . The set of influential nodes identified by SmartInf have the capacity to expose the tweet to a large and diverse population, when targeted as seeds thereby maximizing the influence spread. Experimental evaluation on empirical datasets from Twitter show the superiority of SmartInf over state-of-the-art baselines in terms of infecting larger population; further, our evaluation shows that SmartInf is scalable to large-scale networks and is robust to missing data. Finally, we investigate the key factors behind the improved performance of SmartInf by testing our algorithm on a synthetic network using synthetic cascades simulated on this network. Our results reveal the effectiveness of SmartInf in identifying a diverse set of influential users that facilitate faster diffusion of tweets to a larger population

Temporal Pattern of (Re)tweets Reveal Cascade Migration

Twitter has recently become one of the most popular online social networking websites where users can share news and ideas through messages in the form of tweets. As a tweet gets retweeted from user to user, large cascades of information diffusion are formed over the Twitter follower network. Existing works on cascades have mainly focused on predicting their popularity in terms of size. In this paper, we leverage on the temporal pattern of retweets to model the diffusion dynamics of a cascade. Notably, retweet cascades provide two complementary information: (a) inter-retweet time intervals of retweets, and (b) diffusion of cascade over the underlying follower network. Using datasets from Twitter, we identify two types of cascades based on presence or absence of early peaks in their sequence of inter-retweet intervals. We identify multiple diffusion localities associated with a cascade as it propagates over the network. Our studies reveal the transition of a cascade to a new locality facilitated by pivotal users that are highly cascade dependent following saturation of current locality. We propose an analytical model to show co-occurrence of first peaks and cascade migration to a new locality as well as predict locality saturation from inter-retweet intervals. Finally, we validate these claims from empirical data showing co-occurrence of first peaks and migration with good accuracy; we obtain even better accuracy for successfully classifying saturated and non-saturated diffusion localities from inter-retweet intervals