Spectral learning algorithm reveals propagation capability of complex networks

In network science and the data mining field, a long-lasting and significant task is to predict the propagation capability of nodes in a complex network. Recently, an increasing number of unsupervised learning algorithms, such as the prominent PageRank (PR) and LeaderRank (LR), have been developed to address this issue. However, in degree uncorrelated networks, this paper finds that PR and LR are actually proportional to in-degree of nodes. As a result, the two algorithms fail to accurately predict the nodes' propagation capability. To overcome the arising drawback, this paper proposes a new iterative algorithm called SpectralRank (SR), in which the nodes' propagation capability is assumed to be proportional to the amount of its neighbors after adding a ground node to the network. Moreover, a weighted SR algorithm is also proposed to further involve a priori information of a node itself. A probabilistic framework is established, which is provided as the theoretical foundation of the proposed algorithms. Simulations of the susceptible-infected-removed model on 32 networks, including directed, undirected, and binary ones, reveal the advantages of the SR-family methods (i.e., weighted and unweighted SR) over PR and LR. When compared with other 11 well-known algorithms, the indices in the SR-family always outperform the others. Therefore, the proposed measures provide new insights on the prediction of the nodes' propagation capability and have great implications in the control of spreading behaviors in complex networks.