Amb motiu del tancament d'estiu, la validació de documents es reprendrà a partir del 28 d'agost de 2026. Disculpeu les molèsties.
Con motivo del cierre de verano, la validación de documentos se reanudará a partir del 28 de agosto de 2026. Disculpad las molestias
Due to the summer closure, document validation will resume starting August 28, 2026. We apologize for any inconvenience.

Files

633701.pdf (2.01 MB)

Document type

Article

Version

Published version

Publication date

2014

All rights reserved

Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/50943

Percolation of spatially constrained Erdos-R enyi networks with degree correlations

Journal Title

Authors

Director/Tutor

Journal ISSN

Volume Title

Related resource

http://dx.doi.org/10.1103/PhysRevE.89.012116

Abstract

Motivated by experiments on activity in neuronal cultures [J. Soriano, M. Rodr ́ıguez Mart́ınez, T. Tlusty, and E. Moses, Proc. Natl. Acad. Sci. 105, 13758 (2008)], we investigate the percolation transition and critical exponents of spatially embedded Erd̋os-Ŕenyi networks with degree correlations. In our model networks, nodes are randomly distributed in a two-dimensional spatial domain, and the connection probability depends on Euclidian link length by a power law as well as on the degrees of linked nodes. Generally, spatial constraints lead to higher percolation thresholds in the sense that more links are needed to achieve global connectivity. However, degree correlations favor or do not favor percolation depending on the connectivity rules. We employ two construction methods to introduce degree correlations. In the first one, nodes stay homogeneously distributed and are connected via a distance- and degree-dependent probability. We observe that assortativity in the resulting network leads to a decrease of the percolation threshold. In the second construction methods, nodes are first spatially segregated depending on their degree and afterwards connected with a distance-dependent probability. In this segregated model, we find a threshold increase that accompanies the rising assortativity. Additionally, when the network is constructed in a disassortative way, we observe that this property has little effect on the percolation transition.

Subject

Percolació (Física estadística), Neurociències, Topologia, Dinàmica, Xarxes socials, Xarxes neuronals (Neurobiologia)

Subject (English)

Percolation (Statistical physics), Neurosciences, Topology, Dynamics, Social networks, Neural networks (Neurobiology)

Citation

Collections

Articles publicats en revistes (Física Quàntica i Astrofísica)

Citation

SCHMELTZER, C., et al. Percolation of spatially constrained Erdos-R enyi networks with degree correlations. Physical Review E. 2014. Vol. 89, num. 012116-1-012116-10. ISSN 1539-3755. [consulted: 16 of August of 2026]. Available at: https://hdl.handle.net/2445/50943

Export metadata

JSON - METS

Share record