Networks offer a powerful approach to modeling complex systems by representing the underlying set of pairwise interactions. Link prediction is the task that predicts links of a network that are not directly visible, with profound applications in biological, social, and other complex systems. Despite intensive utilization of the topological feature in this task, it is unclear to what extent a feature can be leveraged to infer missing links. Here, we aim to unveil the capability of a topological feature in link prediction by identifying its prediction performance upper bound. We introduce a theoretical framework that is compatible with different indexes to gauge the feature, different prediction approaches to utilize the feature, and different metrics to quantify the prediction performance. The maximum capability of a topological feature follows a simple yet theoretically validated expression, which only depends on the extent to which the feature is held in missing and nonexistent links. Because a family of indexes based on the same feature shares the same upper bound, the potential of all others can be estimated from one single index. Furthermore, a feature’s capability is lifted in the supervised prediction, which can be mathematically quantified, allowing us to estimate the benefit of applying machine learning algorithms. The universality of the pattern uncovered is empirically verified by 550 structurally diverse networks. The findings have applications in feature and method selection, and shed light on network characteristics that make a topological feature effective in link prediction.

Many spreading processes in our real-life can be considered as a complex contagion, and the linear threshold (LT) model is often applied as a very representative model for this mechanism. Despite its intensive usage, the LT model suffers several limitations in describing the time evolution of the spreading. First, the discrete-time step that captures the speed of the spreading is vaguely defined. Second, the synchronous updating rule makes the nodes infected in batches, which cannot take individual differences into account. Finally, the LT model is incompatible with existing models for the simple contagion. Here, we consider a generalized linear threshold (GLT) model for the continuous-time stochastic complex contagion process that can be efficiently implemented by the Gillespie algorithm. The time in this model has a clear mathematical definition, and the updating order is rigidly defined. We find that the traditional LT model systematically underestimates the spreading speed and the randomness in the spreading sequence order. We also show that the GLT model works seamlessly with the susceptible-infected or susceptible-infected-recovered model. One can easily combine them to model a hybrid spreading process in which simple contagion accumulates the critical mass for the complex contagion that leads to the global cascades. Overall, the GLT model we proposed can be a useful tool to study complex contagion, especially when studying the time evolution of the spreading.

Most real-world systems evolve over time in which entities and the interactions between entities are added and removed—new entities or relationships appear and old entities or relationships vanish. While most network evolutionary models can provide an iterative process for constructing global properties, they cannot capture the evolutionary mechanisms of real systems. Link prediction is hence proposed to predict future links which also can help us understand the evolution law of real systems. The aim of link prediction is to uncover missing links from known parts of the network or quantify the likelihood of the emergence of future links from current structures of the network. However, almost all existing studies ignored that old nodes tend to disappear and new nodes appear over time in real networks, especially in social networks. It is more challenging for link prediction since the new nodes do not have pre-existing structure information. To solve the temporal link prediction problems with new nodes, here we take into account nodal attribute similarity and the shortest path length, namely, ASSPL, to predict future links with new nodes. The results tested on scholar social network and academic funding networks show that it is highly effective and applicable for ASSPL in funding networks with time-evolving. Meanwhile, we make full use of an efficient parameter to exploit how network structure or nodal attribute has an impact on the performance of temporal link prediction. Finally, we find that nodal attributes and network structure complement each other well for predicting future links with new nodes in funding networks.

The co-occurrence association is widely observed in many empirical data. Mining the information in co-occurrence data is essential for advancing our understanding of systems such as social networks, ecosystems, and brain networks. Measuring similarity of entities is one of the important tasks, which can usually be achieved using a network-based approach. Here, we show that traditional methods based on the aggregated network can bring unwanted indirect relationships. To cope with this issue, we propose a similarity measure based on the ego network of each entity, which effectively considers the change of an entity’s centrality from one ego network to another. The index proposed is easy to calculate and has a clear physical meaning. Using two different data sets, we compare the new index with other existing ones. We find that the new index outperforms the traditional network-based similarity measures, and it can sometimes surpass the embedding method. In the meanwhile, the measure by the new index is weakly correlated with those by other methods, hence providing a different dimension to quantify similarities in co-occurrence data. Altogether, our work makes an extension in the network-based similarity measure and can be potentially applied in several related tasks.

Scientist collaboration is of great significance for knowledge production and scientific development, and the prediction of connection and the intensity in collaboration networks are essential to understand collaboration relationships between scientists. In previous studies, most scholars only use local structure similarity to infer scientist collaboration modes, which leads to failure to accurately predict collaboration relationships between scientists. In this study, we propose a prediction method to identify missing links and link weight by using multiple motif features. The experimental results show that the highest improvement of performance in link prediction is 13.5%, and 86.8% in weight prediction. In addition, the correlation analysis on multiple motif features reveals topology correlation between different scientist collaboration modes. Our finding is helpful to predict link possibility and tie strength in scientist collaboration networks more accurately and understand deeply the evolution pattern of collaboration networks among scientists.

In the real world, pathogens do not exist in isolation. The transmission of one pathogen may be affected by the presence of other pathogens, and certain pathogens generate multiple strains with different spreading features. Hence, the behavior of multi-pathogen transmission has attracted much attention in epidemiological research. In this paper, we use the pairwise approximation method to formulate two-pathogen models capturing cross-immunity, super-infection, and co-infection phenomena, in which each pathogen follows a susceptible-infected-susceptible (SIS) mechanism. For each model, we calculate the basic reproduction number and analyze the stability of equilibria, and discuss the differences from the mean-field approach. We demonstrate that simulations are in good agreement with the analytical results.