Burstiness and spreading on temporal networks

Abstract

We discuss how spreading processes on temporal networks are impacted by the shape of their inter-event time distributions. Through simple mathematical arguments and toy examples, we find that the key factor is the ordering in which events take place, a property that tends to be affected by the bulk of the distributions and not only by their tail, as usually considered in the literature. We show that a detailed modeling of the temporal patterns observed in complex networks can change dramatically the properties of a spreading process, such as the ergodicity of a random walk process or the persistence of an epidemic.

Temporal pattern of online communication spike trains in spreading a scientific rumor: how often, who interacts with whom?

“…The time series of user activities, e.g., posting a tweet and replying to a message, are quite distinct from uncorrelated (Poisson random) dynamics in the presence of burstiness [18][19][20], temporal correlations [6,21,22], and non-stationarity of human daily rhythm [23,24], which has significant implications. Diffusion on a temporal network cannot be accurately described by models on static networks and consequently the process presents non-Markovian features with strong influence on the time required to explore the system [25,26]. Furthermore, the dynamics drives a strong heterogeneity observed in user activity [27,28] and user/content popularity [29][30][31].…”

Backtracking and Mixing Rate of Diffusion on Uncorrelated Temporal Networks

“…This effect should be further amended by the effect of triangles or longer cycles, likely leading to a further asymptotic slowdown of the diffusion. This is a new mechanism for the impact of network temporality on diffusive processes, adding to intrinsically different mechanisms such as the bus paradox, where a walker may sit on a node for a very long time [11,19], and the further fact that the mixing time of bursty walker may be much larger than the naive estimate given by the number of jumps required to explore the network multiplied by the average waiting time of the walker at each step [20]. This is a tribute to the extraordinary richness of phenomena brought by the sole departure from a Poisson or discrete-time diffusion process.…”

“…The observation that g(t) may have very different moments from f (t), for instance a much larger mean is known under the name of bus paradox, or inspection paradox [19]. In a popular example, one may think of someone arriving at a bus stop and having to wait (mean of g) for a bus much longer than the mean inter-arrival time between two buses (mean of f ).…”

“…Second, we estimate the impact of the resulting bias to backtrack on the mixing rate of the process. Taken together, these results allow to quantify a mechanism that may either slow down or accelerate diffusion, by changing the number of steps leading to mixing, which is inherently different from well-known mechanisms such as the bus paradox [19] or other temporal mechanisms [20], only affecting the time to relaxation, and not the number of steps. Our observations also allow us to gain insight into unexpected properties of a standard null model for temporal network analysis.…”

Collective iteration behavior for online social networks

“…Collective behaviors of online users have been extensively investigated, which is of great significance for identifying the human communication patterns [1][2][3]. Oliveira et al [4] found the scaling-law in Darwin's and Einstein's correspondence patterns.…”