Discrimination reveals reconstructability of multiplex networks from partial observations

Mincheng Wu, Jiming Chen, Shibo He, Youxian Sun, Shlomo Havlin, Jianxi Gao

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7 Scopus citations


An excellent method for predicting links in multiplex networks is reflected in its ability to reconstruct them accurately. Although link prediction methods perform well on estimating the existence probability of each potential link in monoplex networks by the set of partially observed links, we lack a mathematical tool to reconstruct the multiplex network from the observed aggregate topology and partially observed links in multiplex networks. Here, we fill this gap by developing a theoretical and computational framework that builds a probability space containing possible structures with a maximum likelihood estimation. Then, we discovered that the discrimination, an indicator quantifying differences between layers from an entropy perspective, determines the reconstructability, i.e., the accuracy of such reconstruction. This finding enables us to design the optimal strategy to allocate the set of observed links in different layers for promoting the optimal reconstruction of multiplex networks. Finally, the theoretical analyses are corroborated by empirical results from biological, social, engineered systems, and a large volume of synthetic networks.

Original languageEnglish
Article number163
JournalCommunications Physics
Issue number1
StatePublished - Dec 2022

Bibliographical note

Publisher Copyright:
© 2022, The Author(s).


We thank Prof. H. Eugene Stanley for enlightening discussions and constructive suggestions. We would like to additionally thank the anonymous reviewers for their comprehensive feedback. This work was supported by NSFC 62088101 Autonomous Intelligent Unmanned Systems, NSFC under grant No. U1909207, and Key Research and Development Program of Zhejiang Province (Grant No. 2021C03037). Shlomo H. thanks the Israel Science Foundation (Grant No. 189/19), the NSF-BSF (Grant No. 2019740), the EU H2020 project RISE (Project No. 821115), the EU H2020 DIT4TRAM, and DTRA (Grant No. HDTRA-1-19-1-0016) for financial support. J.G. acknowledges the support of the U.S. National Science Foundation under Grant No. 2047488 and the Rensselaer-IBM AI Research Collaboration.

FundersFunder number
EU H2020821115
EU H2020 DIT4TRAMHDTRA-1-19-1-0016
National Science Foundation2047488
Key Technology Research and Development Program of Shandong2021C03037
National Natural Science Foundation of China62088101, U1909207
Israel Science Foundation189/19


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