Hypergraphs that can depict interactions beyond pairwise edges have emerged as an appropriate representation for modeling polyadic relations in complex systems. With the recent surge of interest in researching hypergraphs, the centrality problem has attracted much attention due to the challenge of how to utilize higher-order structure for the definition of centrality metrics. In this paper, we propose a new centrality method (HGC) on the basis of the gravity model as well as a semi-local HGC, which can achieve a balance between accuracy and computational complexity. Meanwhile, two comprehensive evaluation metrics, i.e., a complex contagion model in hypergraphs, which mimics the group influence during the spreading process and network $s$ -efficiency based on the higher-order distance between nodes, are first proposed to evaluate the effectiveness of our methods. The results show that our methods can filter out nodes that have fast spreading ability and are vital in terms of hypergraph connectivity.

Progress has been made in understanding how temporal network features affect the percentage of nodes reached by an information diffusion process. In this work, we explore further: which node pairs are likely to contribute to the actual diffusion of information, i.e., appear in a diffusion trajectory? How is this likelihood related to the local temporal connection features of the node pair? Such deep understanding of the role of node pairs is crucial to tackle challenging optimization problems such as which kind of node pairs or temporal contacts should be stimulated in order to maximize the prevalence of information spreading. We start by using Susceptible-Infected (SI) model, in which an infected (information possessing) node could spread the information to a susceptible node with a given infection probability β whenever a contact happens between the two nodes, as the information diffusion process. We consider a large number of real-world temporal networks. First, we propose the construction of an information diffusion backbone G_B(β) for a SI spreading process with an infection probability β on a temporal network. The backbone is a weighted network where the weight of each node pair indicates how likely the node pair appears in a diffusion trajectory starting from an arbitrary node. Second, we investigate the relation between the backbones with different infection probabilities on a temporal network. We find that the backbone topology obtained for low and high infection probabilities approach the backbone G_B(β → 0) and G_B(β = 1), respectively. The backbone G_B(β → 0) equals the integrated weighted network, where the weight of a node pair counts the total number of contacts in between. Finally, we explore node pairs with what local connection features tend to appear in G_B(β = 1), thus actually contribute to the global information diffusion. We discover that a local connection feature among many other features we proposed, could well identify the (high-weight) links in G_B(β = 1). This local feature encodes the time that each contact occurs, pointing out the importance of temporal features in determining the role of node pairs in a dynamic process.

The declaration of COVID-19 as a pandemic has largely amplified the spread of related information on social platforms, such as Twitter, Facebook and WeChat. In this work, we investigate how the disease and information co-evolve in the population. We focus on COVID-19 and its information during the period when the disease was widely spread in China, i.e., from January 25th to March 24th, 2020. The co-evolution between disease and information is explored via the spatial analysis of the two spreading processes. We visualize the geo-location of both disease and information at the province level and find that disease is more geo-localized compared to information. High correlation between disease and information data is observed, and also people care about the spread of disease only when it comes to their neighborhood. Regard to the content of the information, we obtain that positive messages are more negatively correlated with the disease compared to negative and neutral messages. Additionally, two machine learning algorithms, i.e., linear regression and random forest, are introduced to further predict the number of infected using characteristics, such as disease spatial related and information-related features. We obtain that both the disease spatial related characteristics of nearby cities and information-related characteristics can help to improve the prediction accuracy. The methodology proposed in this paper may shed light on new clues of emerging infections prediction.

Temporal networks refer to networks like physical contact networks whose topology changes over time. Predicting future temporal network is crucial e.g., to forecast the epidemics. Existing prediction methods are either relatively accurate but black-box, or white-box but less accurate. The lack of interpretable and accurate prediction methods motivates us to explore what intrinsic properties/mechanisms facilitate the prediction of temporal networks. We use interpretable learning algorithms, Lasso Regression and Random Forest, to predict, based on the current activities (i.e., connected or not) of all links, the activity of each link at the next time step. From the coefficients learned from each algorithm, we construct the prediction backbone network that presents the influence of all links in determining each link's future activity. Analysis of the backbone, its relation to the link activity time series and to the time aggregated network reflects which properties of temporal networks are captured by the learning algorithms. Via six real-world contact networks, we find that the next step activity of a particular link is mainly influenced by (a) its current activity and (b) links strongly correlated in the time series to that particular link and close in distance (in hops) in the aggregated network.

Quantifying structural dissimilarities between networks is a fundamental and challenging problem in network science. Previous network comparison methods are based on the structural features, such as the length of shortest path and degree, which only contain part of the topological information. Therefore, we propose an efficient network comparison method based on network embedding, which considers the global structural information. In detail, we first construct a distance matrix for each network based on the distances between node embedding vectors derived from DeepWalk. Then, we define the dissimilarity between two networks based on Jensen-Shannon divergence of the distance distributions. Experiments on both synthetic and empirical networks show that our method outperforms the baseline methods and can distinguish networks well. In addition, we show that our method can capture network properties, e.g., average shortest path length and link density. Moreover, the experiment of modularity further implies the functionality of our method.