The interplay between ranking and communities in networks
This work addresses the challenge of automatically learning network structures from data, which is relevant for practitioners analyzing complex real-world networks where community and hierarchy interplay is unclear.
The authors tackled the problem of jointly inferring community and hierarchical structures in networks, which are typically studied separately, by developing a generative model that exploits network sparsity for efficiency. They demonstrated that their algorithm accurately retrieves node preferences and identifies subsets with different behaviors, enabling automatic determination of the dominant interaction mechanism in networks without prior structural assumptions.
Community detection and hierarchy extraction are usually thought of as separate inference tasks on networks. Considering only one of the two when studying real-world data can be an oversimplification. In this work, we present a generative model based on an interplay between community and hierarchical structures. It assumes that each node has a preference in the interaction mechanism and nodes with the same preference are more likely to interact, while heterogeneous interactions are still allowed. The sparsity of the network is exploited for implementing a more efficient algorithm. We demonstrate our method on synthetic and real-world data and compare performance with two standard approaches for community detection and ranking extraction. We find that the algorithm accurately retrieves the overall node's preference in different scenarios, and we show that it can distinguish small subsets of nodes that behave differently than the majority. As a consequence, the model can recognize whether a network has an overall preferred interaction mechanism. This is relevant in situations where there is no clear "a priori" information about what structure explains the observed network datasets well. Our model allows practitioners to learn this automatically from the data.