Temporal networks are networks whose topology changes over time. Two nodes in a temporal network are connected at a discrete time step only if they have a contact/interaction at that time. The classic temporal network prediction problem aims to predict the temporal network one time step ahead based on the network observed in the past of a given duration. This problem has been addressed mostly via machine learning algorithms, at the expense of high computational costs and limited interpretation of the underlying mechanisms that form the networks. Hence, we propose to predict the connection of each node pair one step ahead based on the connections of this node pair itself and of node pairs that share a common node with this target node pair in the past. The concrete design of our two prediction models is based on the analysis of the memory property of real-world physical networks, i.e., to what extent two snapshots of a network at different times are similar in topology (or overlap). State-of-the-art prediction methods that allow interpretation are considered as baseline models. In seven real-world physical contact networks, our methods are shown to outperform the baselines in both prediction accuracy and computational complexity. They perform better in networks with stronger memory. Importantly, our models reveal how the connections of different types of node pairs in the past contribute to the connection estimation of a target node pair. Predicting temporal networks like physical contact networks in the long-term future beyond short-term i.e., one step ahead is crucial to forecast and mitigate the spread of epidemics and misinformation on the network. This long-term prediction problem has been seldom explored. Therefore, we propose basic methods that adapt each aforementioned prediction model to address classic short-term network prediction problem for long-term network prediction task. The prediction quality of all adapted models is evaluated via the accuracy in predicting each network snapshot and in reproducing key network properties. The prediction based on one of our models tends to have the highest accuracy and lowest computational complexity.

Human social interactions are typically recorded as time-specific dyadic interactions, and represented as evolving (temporal) networks, where links are activated/deactivated over time. However, individuals can interact in groups of more than two people. Such group interactions can be represented as higher-order events of an evolving network. Here, we propose methods to characterize the temporal-topological properties of higher-order events to compare networks and identify their (dis)similarities. We analyzed 8 real-world physical contact networks, finding the following: (a) Events of different orders close in time tend to be also close in topology; (b) Nodes participating in many different groups (events) of a given order tend to involve in many different groups (events) of another order; Thus, individuals tend to be consistently active or inactive in events across orders; (c) Local events that are close in topology are correlated in time, supporting observation (a). Differently, in 5 collaboration networks, observation (a) is almost absent; Consistently, no evident temporal correlation of local events has been observed in collaboration networks. Such differences between the two classes of networks may be explained by the fact that physical contacts are proximity based, in contrast to collaboration networks. Our methods may facilitate the investigation of how properties of higher-order events affect dynamic processes unfolding on them and possibly inspire the development of more refined models of higher-order time-varying networks.

Many real-world complex systems including human interactions can be represented by temporal (or evolving) networks, where links activate or deactivate over time. Characterizing temporal networks is crucial to compare different real-world networks and to detect their common patterns or differences. A systematic method that can characterize simultaneously the temporal and topological relations of the time-specific interactions (also called contacts or events) of a temporal network, is still missing. In this article, we propose a method to characterize to what extent contacts that happen close in time occur also close in topology. Specifically, we study the interrelation between temporal and topological properties of the contacts from three perspectives: (1) the correlation (among the elements) of the activity time series which records the total number of contacts in a network that happen at each time step; (2) the interplay between the topological distance and time difference of two arbitrary contacts; (3) the temporal correlation of contacts within the local neighbourhood centred at each link (so-called ego-network) to explore whether such contacts that happen close in topology are also close in time. By applying our method to 13 real-world temporal networks, we found that temporal-Topological correlation of contacts is more evident in virtual contact networks than in physical contact networks. This could be due to the lower cost and easier access of online communications than physical interactions, allowing and possibly facilitating social contagion, that is, interactions of one individual may influence the activity of its neighbours. We also identify different patterns between virtual and physical networks and among physical contact networks at, for example, school and workplace, in the formation of correlation in local neighbourhoods. Patterns and differences detected via our method may further inspire the development of more realistic temporal network models, that could reproduce jointly temporal and topological properties of contacts.

In this work, we explore the possibility of using a heterogeneous Susceptible-Infected-Susceptible SIS spreading process on an airline network to model airport congestion contagion with the objective to reproduce airport vulnerability. We derive the vulnerability of each airport from the US Airport Network data as the congestion probability of each airport. In order to capture diverse flight features between airports, e.g. frequency and duration, we construct three types of airline networks. The infection rate of each link in the SIS spreading process is proportional to its corresponding weight in the underlying airline network constructed. The recovery rate of each node is also heterogeneous, dependent on its node strength in the underlying airline network, which is the total weight of the links incident to the node. Such heterogeneous recovery rate is motivated by the fact that large airports may recover fast from congestion due to their well-equipped infrastructures. The nodal infection probability in the meta-stable state is used as a prediction of the vulnerability of the corresponding airport. We illustrate that our model could reproduce the distribution of nodal vulnerability and rank the airports in vulnerability evidently better than the SIS model whose recovery rate is homogeneous. The vulnerability is the largest at airports whose strength in the airline network is neither too large nor too small. This phenomenon can be captured by our heterogeneous model, but not the homogeneous model where a node with a larger strength has a higher infection probability. This explains partially the out-performance of the heterogeneous model. This proposed congestion contagion model may shed lights on the development of strategies to identify vulnerable airports and to mitigate global congestion by e.g. congestion reduction at selected airports.

We model airport congestion contagion as an SIS spreading process on an airport transportation network to explain airport vulnerability. The vulnerability of each airport is derived from the US Airport Network data as its congestion probability. We construct three types of airline networks to capture diverse features such as the frequency and duration of flights. The weight of each link augments its infection rate in SIS spreading process. The nodal infection probability in the meta-stable state is used as estimate the vulnerability of the corresponding airport. We illustrate that our model could reasonably capture the distribution of nodal vulnerability and rank airports in vulnerability evidently better than the random ranking, but not significantly better than using nodal network properties. Such congestion contagion model not only allows the identification of vulnerable airports but also opens the possibility to reduce global congestion via congestion reduction in few airports.