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Diversification-constrained bipartite network null model with maximum entropy and its numerical solution

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  • Wang, Xuhui
  • Ye, Wuyi

Abstract

The network null model is a statistical framework for making inferences about complex network systems based on partially observed attributes, identifying statistically significant patterns within networks. This study extends the null model for weighted bipartite networks by introducing diversification heterogeneity constraints (measured via the Herfindahl–Hirschman index) within the maximum entropy framework. Compared to traditional degree- or strength-constrained null models, our approach captures edge weight dispersion heterogeneity and could find broad application in ecology, economics, and management science. To address the associated numerical challenges, we develop a low-rank initialization scheme and an alternating optimization algorithm. Simulation study confirms the distinctive advantages of the new model and the effectiveness of the numerical solution. In addition, our empirical analysis shows that China’s financial institutions’ overlapping equity investment can be reproduced by the proposed model.

Suggested Citation

  • Wang, Xuhui & Ye, Wuyi, 2026. "Diversification-constrained bipartite network null model with maximum entropy and its numerical solution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 689(C).
    • Handle: RePEc:eee:phsmap:v:689:y:2026:i:c:s0378437126001718
    DOI: 10.1016/j.physa.2026.131435
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