Resolution of ranking hierarchies in directed networks

Identifying ranking hierarchies in complex networks is of paramount importance in many disciplines and applications

PLOS ONE 13, 2 (2018)

E. Letizia, P. Barucca, F. Lillo

LQ placeholderIdentifying ranking hierarchies in complex networks is of paramount importance in many disciplines
and applications

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.

LQ placeholderNetwork valuation in financial systems

Network valuation in financial systems

P. Barucca, M. Bardoscia, F. Caccioli, M. D’Errico, G. Visentin, G. Caldarelli, S. Battiston

Mathematical Finance

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The space of functions computed by deep layered machines

A. Mozeika, B. Li, D. Saad

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Replica analysis of overfitting in generalized linear models

T. Coolen, M. Sheikh, A. Mozeika, F. Aguirre-Lopez, F. Antenucci

Sub. to Journal of Physics A

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Taming complexity

M. Reeves, S. Levin, T. Fink, A. Levina

Harvard Business Review

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Replica analysis of Bayesian data clustering

A. Mozeika, T. Coolen

Journal of Physics A

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F. Vanni, P. Barucca

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