Abstract

We focus on spatially-extended networks during their transition from short-range connectivities to a scale-free structure expressed by heavy-tailed degree-distribution. In particular, a model is introduced for the generation of such graphs, which combines spatial growth and preferential attachment. In this model the transition to heterogeneous structures is always accompanied by a change in the graph’s degree-degree correlation properties: while high assortativity levels characterize the dominance of short distance couplings, long-range connectivity structures are associated with small amounts of disassortativity. Our results allow to infer that a disassortative mixing is essential for establishing long-range links. We discuss also how our findings are consistent with recent experimental studies of 2-dimensional neuronal cultures.

Details

Title
Assortative mixing in spatially-extended networks
Author
Makarov, Vladimir V 1 ; Kirsanov, Daniil V 1 ; Frolov, Nikita S 2   VIAFID ORCID Logo  ; Maksimenko, Vladimir A 1 ; Li, Xuelong 3 ; Wang, Zhen 4   VIAFID ORCID Logo  ; Hramov, Alexander E 2   VIAFID ORCID Logo  ; Boccaletti, Stefano 5 

1  REC ‘Artificial Intelligence Systems and Neurotechnology’, Yurij Gagarin State Technical University of Saratov, Saratov, Russia 
2  REC ‘Artificial Intelligence Systems and Neurotechnology’, Yurij Gagarin State Technical University of Saratov, Saratov, Russia; Faculty of Nonlinear Processes, Saratov State University, Saratov, Russia 
3  Xi’an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi’an, Shaanxi, China 
4  School of Mechanical Engineering and Center for OPTical IMagery Analysis and Learning (OPTIMAL), Northwestern Polytechnical University, Xi’an, Shaanxi, China 
5  CNR-Institute of Complex Systems, Via Madonna del Piano 10, 50019 Sesto Fiorentino, Florence, Italy; Unmanned Systems Research Institute, Northwestern Polytechnical University, Xi’an, Shaanxi, China 
Pages
1-8
Publication year
2018
Publication date
Sep 2018
Publisher
Nature Publishing Group
e-ISSN
20452322
Source type
Scholarly Journal
Language of publication
English
DOI
https://doi.org/10.1038/s41598-018-32160-4
ProQuest document ID
2104154237
Copyright
© 2018. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.