The higher-order structure of networks is a hot research topic in complex networks. It has received much attention because it is closely related to the functionality of networks, such as network transportation and propagation. For instance, recent studies have revealed that studying higher-order networks can explore hub structures in transportation networks and information dissemination units in neuronal networks. Therefore, the destruction of the connectivity of higher-order networks will cause significant damage to network functionalities. Meanwhile, previous works pointed out that the function of a complex network depends on the giant component of the original(low-order) network. Therefore, the network functionality will be influenced by both the low-order and its corresponding higher-order network. To study this issue, we build a network model of the interdependence of low-order and higher-order networks (we call it ILH). When some low-order network nodes fail, the low-order network’s giant component shrinks, leading to changes in the structure of the higher-order network, which further affects the low-order network. This process occurs iteratively; the propagation of the failure can lead to an eventual network crash. We conducted experiments on different networks based on the percolation theory, and our network percolation results demonstrated a first-order phase transition feature. In particular, we found that an ILH is more fragile than the low-order network alone, and an ILH is more likely to be corrupted in the event of a random node failure.
Link prediction plays an important role in information filtering and numerous research works have been made in this field. However, traditional link prediction algorithms mainly focus on overall prediction accuracy, ignoring the heterogeneity of the prediction accuracy for different links. In this paper, we analyzed the prediction accuracy of each link in networks and found that the prediction accuracy for different links is severely polarized. Further analysis shows that the accuracy of edges with low edge betweenness is consistently high while that of edges with high edge betweenness is consistently low, i.e. AUC follows a bimodal distribution with one peak around 0.5 and the other peak around 1. Our results indicate that link prediction algorithms should focus more on edges with high betweenness instead of edges with low betweenness. To improve the accuracy of edges with high betweenness, we proposed an improved algorithm called RA_LP which takes advantage of resource transfer of the second-order and third-order paths of local path. Results show that this algorithm can improve the link prediction accuracy for edges with high betweenness as well as the overall accuracy.
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