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Makarov VV, Kirsanov DV, Frolov NS, Maksimenko VA, Li X, Wang Z, Hramov AE, Boccaletti S. Assortative mixing in spatially-extended networks. Sci Rep 2018; 8:13825. [PMID: 30218078 PMCID: PMC6138734 DOI: 10.1038/s41598-018-32160-4] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/11/2018] [Accepted: 08/20/2018] [Indexed: 11/17/2022] Open
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.
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Affiliation(s)
- Vladimir V Makarov
- REC 'Artificial Intelligence Systems and Neurotechnology', Yurij Gagarin State Technical University of Saratov, Polytechnicheskaja str 77, 410054, Saratov, Russia
| | - Daniil V Kirsanov
- REC 'Artificial Intelligence Systems and Neurotechnology', Yurij Gagarin State Technical University of Saratov, Polytechnicheskaja str 77, 410054, Saratov, Russia
| | - Nikita S Frolov
- REC 'Artificial Intelligence Systems and Neurotechnology', Yurij Gagarin State Technical University of Saratov, Polytechnicheskaja str 77, 410054, Saratov, Russia
- Faculty of Nonlinear Processes, Saratov State University, Astrakhanskaja str. 83, 410012, Saratov, Russia
| | - Vladimir A Maksimenko
- REC 'Artificial Intelligence Systems and Neurotechnology', Yurij Gagarin State Technical University of Saratov, Polytechnicheskaja str 77, 410054, Saratov, Russia
| | - Xuelong Li
- Xi'an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi'an, 710119, Shaanxi, China
| | - Zhen Wang
- School of Mechanical Engineering and Center for OPTical IMagery Analysis and Learning (OPTIMAL), Northwestern Polytechnical University, Xi'an, 710072, Shaanxi, China
| | - Alexander E Hramov
- REC 'Artificial Intelligence Systems and Neurotechnology', Yurij Gagarin State Technical University of Saratov, Polytechnicheskaja str 77, 410054, Saratov, Russia.
- Faculty of Nonlinear Processes, Saratov State University, Astrakhanskaja str. 83, 410012, Saratov, Russia.
| | - Stefano Boccaletti
- CNR-Institute of Complex Systems, Via Madonna del Piano 10, 50019 Sesto Fiorentino, Florence, Italy
- Unmanned Systems Research Institute, Northwestern Polytechnical University, Xi'an, 710072, Shaanxi, China
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