Dose–response functions and surrogate models for exploring social contagion in the Copenhagen Networks Study

Spreading dynamics and complex contagion processes on networks are important mechanisms underlying the emergence of critical transitions, tipping points and other non-linear phenomena in complex human and natural systems. Increasing amounts of temporal network data are now becoming available to study such spreading processes of behaviours, opinions, ideas, diseases and innovations to test hypotheses regarding their specific properties. To this end, we here present a methodology based on dose–response functions and hypothesis testing using surrogate data models that randomise most aspects of the empirical data while conserving certain structures relevant to contagion, group or homophily dynamics. We demonstrate this methodology for synthetic temporal network data of spreading processes generated by the adaptive voter model. Furthermore, we apply it to empirical temporal network data from the Copenhagen Networks Study. This data set provides a physically-close-contact network between several hundreds of university students participating in the study over the course of 3 months. We study the potential spreading dynamics of the health-related behaviour “regularly going to the fitness studio” on this network. Based on a hierarchy of surrogate data models, we find that our method neither provides significant evidence for an influence of a dose–response-type network spreading process in this data set, nor significant evidence for homophily. The empirical dynamics in exercise behaviour are likely better described by individual features such as the disposition towards the behaviour, and the persistence to maintain it, as well as external influences affecting the whole group, and the non-trivial network structure. The proposed methodology is generic and promising also for applications to other temporal network data sets and traits of interest.

Habituation effect in social networks as a potential factor silently crushing influence maximisation efforts

Information spreading processes are a key phenomenon observed within real and digital social networks. Network members are often under pressure from incoming information with different sources, such as informative campaigns for increasing awareness, viral marketing, rumours, fake news, or the results of other activities. Messages are often repeated, and such repetition can improve performance in the form of cumulative influence. Repeated messages may also be ignored due to a limited ability to process information. Learning processes are leading to the repeated messages being ignored, as their content has already been absorbed. In such cases, responsiveness decreases with repetition, and the habituation effect can be observed. Here, we analyse spreading processes while considering the habituation effect and performance drop along with an increased number of contacts. The ability to recover when reducing the number of messages is also considered. The results show that even low habituation and a decrease in propagation probability may substantially impact network coverage. This can lead to a significant reduction in the potential for a seed set selected with an influence maximisation method. Apart from the impact of the habituation effect on spreading processes, we show how it can be reduced with the use of the sequential seeding approach. This shows that sequential seeding is less sensitive to the habituation effect than single-stage seeding, and that it can be used to limit the negative impact on users overloaded with incoming messages.

An Efficient Partition-Based Approach to Identify and Scatter Multiple Relevant Spreaders in Complex Networks

One of the main problems in graph analysis is the correct identification of relevant nodes for spreading processes. Spreaders are crucial for accelerating/hindering information diffusion, increasing product exposure, controlling diseases, rumors, and more. Correct identification of spreaders in graph analysis is a relevant task to optimally use the network structure and ensure a more efficient flow of information. Additionally, network topology has proven to play a relevant role in the spreading processes. In this sense, more of the existing methods based on local, global, or hybrid centrality measures only select relevant nodes based on their ranking values, but they do not intentionally focus on their distribution on the graph. In this paper, we propose a simple yet effective method that takes advantage of the underlying graph topology to guarantee that the selected nodes are not only relevant but also well-scattered. Our proposal also suggests how to define the number of spreaders to select. The approach is composed of two phases: first, graph partitioning; and second, identification and distribution of relevant nodes. We have tested our approach by applying the SIR spreading model over nine real complex networks. The experimental results showed more influential and scattered values for the set of relevant nodes identified by our approach than several reference algorithms, including degree, closeness, Betweenness, VoteRank, HybridRank, and IKS. The results further showed an improvement in the propagation influence value when combining our distribution strategy with classical metrics, such as degree, outperforming computationally more complex strategies. Moreover, our proposal shows a good computational complexity and can be applied to large-scale networks.

Path-integral formulation of spreading processes in complex networks

We introduce a path-integral formulation of network-based measures that generalize the concept of geodesic distance and that provides fundamental insights into the dynamics of disease transmission as well as an efficient numerical estimation of the infection arrival time.