The interplay between ranking and communities in networks

TL;DR

This paper introduces a generative model that jointly considers community and hierarchical structures in networks, enabling more accurate detection of node preferences and interaction mechanisms, especially in complex real-world data.

Contribution

It presents a novel model that captures the interplay between community and hierarchy, improving inference of node preferences and interaction types in networks.

Findings

Accurately retrieves node preferences in various scenarios.

Distinguishes small subsets of nodes with different behaviors.

Identifies overall preferred interaction mechanisms in networks.

Abstract

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.