Link prediction is the problem of predicting the location of either unknown or fake links from uncertain structural information of a network. Link prediction algorithms are useful in gaining insight into different network structures from partial observations of exemplars. However, existing link prediction algorithms only focus on regular complex networks and are overly dependent on either the closed triangular structure of networks or the so-called preferential attachment phenomenon. The performance of these algorithms on highly sparse or treelike networks is poor. In this letter, we proposed a method that is based on the network heterogeneity. We test our algorithms for three real large sparse networks: a metropolitan water distribution network, a Twitter network, and a sexual contact network. We find that our method is effective and performs better than traditional algorithms, especially for the Twitter network. We further argue that heterogeneity is the most obvious defining pattern for complex networks, while other statistical properties failed to be predicted. Moreover, preferential attachment based link prediction performed poorly and hence we infer that preferential attachment is not a plausible model for the genesis of many networks. We also suggest that heterogeneity is an important mechanism for online information propagation.

Link prediction is the problem of predicting the existence and location of unknown links from uncertain structural information of a network. Most existing accuracy measures do not consider the role of time evolution within the network. Moreover, almost all existing methods use indirect links to infer and evaluate the validity of links. We introduce time as a parameter for link prediction accuracy measures, and we modify the structure of the link prediction algorithms to exploit information of the known direct links for link prediction. We find that the direct link algorithm performs better than the indirect link algorithm for a range of time varying networks. We show that the network structure plays a more important role than weights for links prediction. In addition, our analysis finds that the number of common neighbours also plays an important role for the so-called weak-ties phenomenon.

Evolution and popularity are two keys of the Barabasi–Albert model, which generates a power law distribution of network degrees. Evolving network generation models are important as they offer an explanation of both how and why complex networks (and scale-free networks, in particular) are ubiquitous. We adopt the evolution principle and then propose a very simple and intuitive new model for network growth, which naturally evolves modular networks with multiple communities. The number and size of the communities evolve over time and are primarily subjected to a single free parameter. Surprisingly, under some circumstances, our framework can construct a tree-like network with clear community structures—branches and leaves of a tree. Results also show that new communities will absorb a link resource to weaken the degree growth of hub nodes. Our models have a common explanation for the community of regular and tree-like networks and also breaks the tyranny of the early adopter; unlike the standard popularity principle, newer nodes and communities will come to dominance over time. Importantly, our model can fit well with the construction of the SARS-Cov-2 haplotype evolutionary network.