Nonreciprocal random networks and their percolation properties

Fuente: arXiv
Saved in:
Bibliographic Details
Main Author: Steinbock, Chanania
Format: Preprint
Published: 2025
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866914077185409024
author Steinbock, Chanania
author_facet Steinbock, Chanania
contents We study the effects of nonreciprocity and network structure on percolation. To this end, we investigate nonreciprocal random networks - directed networks for which the probability of a link occurring from node i to node j differs from the probability of the reverse link occurring from node j to node i. We analytically determine the degree and percolation properties of such networks with exactly two types of link probability, demonstrating that whether the networks are structured such that the nodes are not statistically indistinguishable has profound effects on these measures, both quantitively and in how such networks need to be approached. In particular, we develop a technique for solving the percolation problem which can be applied to both structured and unstructured networks. The method entails writing self-consistent integral and differential equations for the probability that each node will belong to the network's giant component. Exact solutions to these equations are obtained and simulations which confirm our analytic predictions are presented.
format Preprint
id arxiv_https___arxiv_org_abs_2509_05253
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Nonreciprocal random networks and their percolation properties
Steinbock, Chanania
Statistical Mechanics
Disordered Systems and Neural Networks
Physics and Society
We study the effects of nonreciprocity and network structure on percolation. To this end, we investigate nonreciprocal random networks - directed networks for which the probability of a link occurring from node i to node j differs from the probability of the reverse link occurring from node j to node i. We analytically determine the degree and percolation properties of such networks with exactly two types of link probability, demonstrating that whether the networks are structured such that the nodes are not statistically indistinguishable has profound effects on these measures, both quantitively and in how such networks need to be approached. In particular, we develop a technique for solving the percolation problem which can be applied to both structured and unstructured networks. The method entails writing self-consistent integral and differential equations for the probability that each node will belong to the network's giant component. Exact solutions to these equations are obtained and simulations which confirm our analytic predictions are presented.
title Nonreciprocal random networks and their percolation properties
topic Statistical Mechanics
Disordered Systems and Neural Networks
Physics and Society
url https://arxiv.org/abs/2509.05253