This paper presents a method for inferring hierarchical structure in networks and using it to predict missing connections. Networks are often hierarchical, with vertices grouping into subgroups at multiple scales. The authors propose a hierarchical random graph model that can capture this structure and explain various network properties, such as degree distributions, clustering coefficients, and path lengths. They demonstrate that this model can accurately predict missing connections in partially known networks, outperforming existing methods. The hierarchical random graph model is based on a dendrogram, a tree-like structure representing hierarchical relationships. Each internal node in the dendrogram is assigned a probability, and edges are added between vertices based on these probabilities. This model can capture both assortative and disassortative structures, as well as arbitrary mixtures of the two, at all scales. The authors apply their method to three example networks: a metabolic network, a terrorist association network, and a grassland food web. They generate resampled networks based on the hierarchical model and find that these networks closely match the statistical properties of the originals, including degree distributions, clustering coefficients, and path lengths. This suggests that hierarchical structure can explain many network features. The method is also used to predict missing connections in networks. By generating a set of hierarchical random graphs that fit the observed network, the authors identify pairs of vertices with high probabilities of connection but no observed edge. These pairs are considered likely candidates for missing connections. The method is tested on the three example networks and shown to outperform existing link prediction methods, particularly in networks with complex structures. The hierarchical model is flexible and can incorporate domain-specific information, such as species traits in food webs or biochemical data. The authors also note that the model can handle false positives in network data, predicting pairs of vertices with low connection probabilities that are actually connected. The study highlights the importance of hierarchical structure in complex networks and shows that it can provide insights into various network phenomena. The method is effective in a wide range of network structures and can be used to predict missing connections with high accuracy. The results suggest that hierarchy is a central organizing principle of complex networks, capable of explaining many network features.This paper presents a method for inferring hierarchical structure in networks and using it to predict missing connections. Networks are often hierarchical, with vertices grouping into subgroups at multiple scales. The authors propose a hierarchical random graph model that can capture this structure and explain various network properties, such as degree distributions, clustering coefficients, and path lengths. They demonstrate that this model can accurately predict missing connections in partially known networks, outperforming existing methods. The hierarchical random graph model is based on a dendrogram, a tree-like structure representing hierarchical relationships. Each internal node in the dendrogram is assigned a probability, and edges are added between vertices based on these probabilities. This model can capture both assortative and disassortative structures, as well as arbitrary mixtures of the two, at all scales. The authors apply their method to three example networks: a metabolic network, a terrorist association network, and a grassland food web. They generate resampled networks based on the hierarchical model and find that these networks closely match the statistical properties of the originals, including degree distributions, clustering coefficients, and path lengths. This suggests that hierarchical structure can explain many network features. The method is also used to predict missing connections in networks. By generating a set of hierarchical random graphs that fit the observed network, the authors identify pairs of vertices with high probabilities of connection but no observed edge. These pairs are considered likely candidates for missing connections. The method is tested on the three example networks and shown to outperform existing link prediction methods, particularly in networks with complex structures. The hierarchical model is flexible and can incorporate domain-specific information, such as species traits in food webs or biochemical data. The authors also note that the model can handle false positives in network data, predicting pairs of vertices with low connection probabilities that are actually connected. The study highlights the importance of hierarchical structure in complex networks and shows that it can provide insights into various network phenomena. The method is effective in a wide range of network structures and can be used to predict missing connections with high accuracy. The results suggest that hierarchy is a central organizing principle of complex networks, capable of explaining many network features.