Quantifying multiple social relationships based on a multiplex stochastic block model


Online social networks have attracted great attention recently, because they make it easy to build social connections for people all over the world. However, the observed structure of an online social network is always the aggregation of multiple social relationships. Thus, it is of great importance for real-world networks to reconstruct the full network structure using limited observations. The multiplex stochastic block model is introduced to describe multiple social ties, where different layers correspond to different attributes (e.g., age and gender of users in a social network). In this letter, we aim to improve the model precision using maximum likelihood estimation, where the precision is defined by the cross entropy of parameters between the data and model. Within this framework, the layers and partitions of nodes in a multiplex network are determined by natural node annotations, and the aggregate of the multiplex network is available. Because the original multiplex network has a high degree of freedom, we add an independent functional layer to cover it, and theoretically provide the optimal block number of the added layer. Empirical results verify the effectiveness of the proposed method using four measures, i.e., error of link probability, cross entropy, area under the receiver operating characteristic curve, and Bayes factor.

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Corresponding author

Correspondence to Shibo He.

Additional information

Project supported by the National Natural Science Foundation of China (No. 61731004)


Mincheng WU and Shibo HE designed the research. Zhen LI and Cunqi SHAO processed the data. Mincheng WU and Zhen LI drafted the manuscript. Shibo HE revised and finalized the paper.

Compliance with ethics guidelines

Mincheng WU, Zhen LI, Cunqi SHAO, and Shibo HE declare that they have no conflict of interest.

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Wu, M., Li, Z., Shao, C. et al. Quantifying multiple social relationships based on a multiplex stochastic block model. Front Inform Technol Electron Eng (2021). https://doi.org/10.1631/FITEE.2000617

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Key words

  • Social network
  • Multiplex network
  • Stochastic block model

CLC number

  • TP3-05