Identifying important nodes based on upstream and downstream time-respecting paths in temporal networks

Identifying the nodes that play significant roles in the epidemic spreading process has attracted extensive attention in recent years. Few centrality measures, such as temporal degree and temporal closeness centrality, have been proposed to quantify node importance based on the topological structure of social contact networks. Most methods estimate the importance of a node from a single aspect, e.g. a higher degree in time snapshot graphs, or shorter distances to other nodes along time-respecting paths. However, this may not be the case in the real world. On the one hand, a node with more nodes on its out streams (i.e. downstream) should be more important because it may affect more nodes along its time-stamped contacting paths once it is infected. On the other hand, a node with more nodes in its in streams (i.e. upstream) deserves closer attention, as it has a higher probability of infection by other nodes. We propose a new temporal centrality measure, upstream and downstream centrality (UD-centrality) with two forms of realizations, i.e. a linear UD-centrality (L-UD) and a product UD-centrality (P-UD) to estimate the importance of nodes based on the temporal structures of social contact networks. We compare our L-UD and P-UD to three classic temporal network centralities through simulations on 14 real-world temporal networks based on the susceptible-infected (SI) model. The comparison results show that UD-centrality can more accurately rank the importance of nodes than the baseline centrality measures.

Spatial utilization predicts animal social contact networks are not scale-free

While heterogeneity in social behaviour has been described in many human contexts it is often assumed to be less common in the animal kingdom even though scale-free networks are observed. This homogeneity raises the question of whether the patterns of behaviour necessary to account for scale-free social contact networks, where the degree distribution follows a power law, i.e. a few individuals are very highly connected but most have only a few connections, occur in animals, or whether other mechanisms are needed to produce realistic contact network architectures. We develop a space-utilization model for individual animal behaviour to predict the individuals' social contact network. Using basic properties of the χ 2 distribution we present a simple analytical result that allows the model to give a range of predictions with minimal computational effort. The model results are tested on data collected in New Zealand for the social contact networks of the wild brushtail possum ( Trichosurus vulpecula ). Our model provides a better prediction of network architecture than other simple models, including a scale-free model.