Activity clocks: spreading dynamics on temporal networks of human contact

Abstract

Dynamical processes on time-varying complex networks are key to understanding and modeling a broad variety of processes in socio-technical systems. Here we focus on empirical temporal networks of human proximity and we aim at understanding the factors that, in simulation, shape the arrival time distribution of simple spreading processes. Abandoning the notion of wall-clock time in favour of node-specific clocks based on activity exposes robust statistical patterns in the arrival times across different social contexts. Using randomization strategies and generative models constrained by data, we show that these patterns can be understood in terms of heterogeneous inter-event time distributions coupled with heterogeneous numbers of events per edge. We also show, both empirically and by using a synthetic dataset, that significant deviations from the above behavior can be caused by the presence of edge classes with strong activity correlations.T he field of complex networks has recently undergone an important evolution. Thanks to the recent availability of time-resolved data sources, many studies performed under the assumption of static network structures can now be extended to take into account the network's dynamics. Data on time-varying networks are becoming accessible across a variety of contexts, ranging from communication networks [1][2][3][4][5][6] to proximity networks 7,8 and infrastructure networks 9,10 . This avalanche of data is prompting a surge of activity in the field of ''temporal networks '' 11 . Data analysis has shown the coexistence of statistically stationary properties and topological changes, as well as the burstiness of interactions characterized by highly skewed distributions of interevent times [1][2][3][4][5][6][7][8][9][10][11][12][13][14] . These temporal features of networks influence the dynamics of network processes, just like the topological structure of static networks does 15 . As a consequence, and similarly to the case of static networks, simple dynamical processes such as random walks 16 , synchronization phenomena 17 , consensus formation 18 or spreading processes [19][20][21][22][23][24][25] can be used as probes to investigate the temporal and structural properties of timevarying networks.Previous works on the dynamics of spreading processes over complex networks have considered both the topological and the temporal structure of networks 11,19,23 , as well as the specific impact that the temporal structure bears on the spreading process. The quantities used to quantify the measured effects are typically network averages, such as the outbreak sizes of an epidemic or its prevalence. These average quantities, however, fail to account for important heterogeneities in the arrival times of the spreading process. Recent work 26 showed that the non-stationarity and burstiness of empirical temporal networks lead to noisy distributions of arrival times, and that shifting the perspective from a global notion of wall-clock time to a node-specific ''time'' based on node activity allows to...

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