Hidden network generating rules from partially observed complex networks

Complex biological, neuroscience, geoscience and social networks exhibit heterogeneous self-similar higher order topological structures that are usually characterized as being multifractal in nature. However, describing their topological complexity through a compact mathematical description and deciphering their topological governing rules has remained elusive and prevented a comprehensive understanding of networks. To overcome this challenge, we propose a weighted multifractal graph model capable of capturing the underlying generating rules of complex systems and characterizing their node heterogeneity and pairwise interactions. To infer the generating measure with hidden information, we introduce a variational expectation maximization framework. We demonstrate the robustness of the network generator reconstruction as a function of model properties, especially in noisy and partially observed scenarios. The proposed network generator inference framework is able to reproduce network properties, differentiate varying structures in brain networks and chromosomal interactions, and detect topologically associating domain regions in conformation maps of the human genome.