Resolution of ranking hierarchies in directed networks

TL;DR

This paper examines the limitations of the agony method in detecting hierarchies in directed networks, introduces a new random graph model to analyze these limits, and proposes an iterative approach to improve hierarchy detection.

Contribution

The paper introduces the Ranked Stochastic Block Model to analyze hierarchy detection limits and proposes an iterated agony method to enhance resolution in weak or small class structures.

Findings

Agony may fail in weak or small class structures

Resolution threshold characterized analytically

Iterated agony partially overcomes resolution limits

Abstract

Identifying hierarchies and rankings of nodes in directed graphs is fundamental in many applications such as social network analysis, biology, economics, and finance. A recently proposed method identifies the hierarchy by finding the ordered partition of nodes which minimises a score function, termed agony. This function penalises the links violating the hierarchy in a way depending on the strength of the violation. To investigate the resolution of ranking hierarchies we introduce an ensemble of random graphs, the Ranked Stochastic Block Model. We find that agony may fail to identify hierarchies when the structure is not strong enough and the size of the classes is small with respect to the whole network. We analytically characterise the resolution threshold and we show that an iterated version of agony can partly overcome this resolution limit.