Ranking nodes in bipartite systems with a non-linear iterative map

Fuente: arXiv
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Main Authors: Mazzolini, Andrea, Caselle, Michele, Osella, Matteo
Format: Preprint
Published: 2024
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author Mazzolini, Andrea
Caselle, Michele
Osella, Matteo
author_facet Mazzolini, Andrea
Caselle, Michele
Osella, Matteo
contents Ranking nodes in networks according to a defined measure of importance is an extensively studied task, with applications in ecology, economic trade networks, and social networks. This paper introduces a method based on a non-linear iterative map to evaluate node relevance in bipartite networks. By tuning a single parameter $γ$, the method captures different concepts of node importance, including established measures like degree centrality, eigenvector centrality and the fitness-complexity ranking. The algorithm's flexibility allows for efficient ranking optimization tailored to specific tasks, outperforming state-of-the-art algorithms. We apply this method to ecological mutualistic networks, where ranking quality can be assessed by the extinction area - the rate at which the system collapses when species are removed in a certain order. The map with the optimal $γ$ value surpasses existing ranking methods on this task. Additionally, our method excels in evaluating nestedness, another crucial structural property of ecological systems, requiring specific node rankings. Finally, we explore theoretical aspects of the map, revealing a phase transition at a critical $γ$ dependent on the data structure that can be characterized analytically for random networks. Near the critical point, the map exhibits unique features and a distinctive "triangular" packing pattern of the incidence matrix.
format Preprint
id arxiv_https___arxiv_org_abs_2406_17572
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Ranking nodes in bipartite systems with a non-linear iterative map
Mazzolini, Andrea
Caselle, Michele
Osella, Matteo
Statistical Mechanics
Physics and Society
Quantitative Methods
Ranking nodes in networks according to a defined measure of importance is an extensively studied task, with applications in ecology, economic trade networks, and social networks. This paper introduces a method based on a non-linear iterative map to evaluate node relevance in bipartite networks. By tuning a single parameter $γ$, the method captures different concepts of node importance, including established measures like degree centrality, eigenvector centrality and the fitness-complexity ranking. The algorithm's flexibility allows for efficient ranking optimization tailored to specific tasks, outperforming state-of-the-art algorithms. We apply this method to ecological mutualistic networks, where ranking quality can be assessed by the extinction area - the rate at which the system collapses when species are removed in a certain order. The map with the optimal $γ$ value surpasses existing ranking methods on this task. Additionally, our method excels in evaluating nestedness, another crucial structural property of ecological systems, requiring specific node rankings. Finally, we explore theoretical aspects of the map, revealing a phase transition at a critical $γ$ dependent on the data structure that can be characterized analytically for random networks. Near the critical point, the map exhibits unique features and a distinctive "triangular" packing pattern of the incidence matrix.
title Ranking nodes in bipartite systems with a non-linear iterative map
topic Statistical Mechanics
Physics and Society
Quantitative Methods
url https://arxiv.org/abs/2406.17572