Global hierarchy vs local structure: Spurious self-feedback in scale-free networks
Networks with fat-tailed degree distributions are omnipresent across many scientific disciplines. Such systems are characterized by so-called hubs, specific nodes with high numbers of connections to other nodes. By this property, they are expected to be key to the collective network behavior, e.g.,...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2021-09-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.3.033272 |
| _version_ | 1797210912619233280 |
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| author | Claudia Merger Timo Reinartz Stefan Wessel Carsten Honerkamp Andreas Schuppert Moritz Helias |
| author_facet | Claudia Merger Timo Reinartz Stefan Wessel Carsten Honerkamp Andreas Schuppert Moritz Helias |
| author_sort | Claudia Merger |
| collection | DOAJ |
| description | Networks with fat-tailed degree distributions are omnipresent across many scientific disciplines. Such systems are characterized by so-called hubs, specific nodes with high numbers of connections to other nodes. By this property, they are expected to be key to the collective network behavior, e.g., in Ising models on such complex topologies. This applies in particular to the transition into a globally ordered network state, which thereby proceeds in a hierarchical fashion, and with a nontrivial local structure. Standard mean-field theory of Ising models on scale-free networks underrates the presence of the hubs, while nevertheless providing remarkably reliable estimates for the onset of global order. Here we expose that a spurious self-feedback effect, inherent to mean-field theory, underlies this apparent paradox. More specifically, we demonstrate that higher order interaction effects precisely cancel the self-feedback on the hubs, and we expose the importance of hubs for the distinct onset of local versus global order in the network. Due to the generic nature of our arguments, we expect the mechanism that we uncover for the archetypal case of Ising networks of the Barabási-Albert type to be also relevant for other systems with a strongly hierarchical underlying network structure. |
| first_indexed | 2024-04-24T10:18:08Z |
| format | Article |
| id | doaj.art-252a095aae0f464a883dc819856ad454 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:18:08Z |
| publishDate | 2021-09-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-252a095aae0f464a883dc819856ad4542024-04-12T17:14:16ZengAmerican Physical SocietyPhysical Review Research2643-15642021-09-013303327210.1103/PhysRevResearch.3.033272Global hierarchy vs local structure: Spurious self-feedback in scale-free networksClaudia MergerTimo ReinartzStefan WesselCarsten HonerkampAndreas SchuppertMoritz HeliasNetworks with fat-tailed degree distributions are omnipresent across many scientific disciplines. Such systems are characterized by so-called hubs, specific nodes with high numbers of connections to other nodes. By this property, they are expected to be key to the collective network behavior, e.g., in Ising models on such complex topologies. This applies in particular to the transition into a globally ordered network state, which thereby proceeds in a hierarchical fashion, and with a nontrivial local structure. Standard mean-field theory of Ising models on scale-free networks underrates the presence of the hubs, while nevertheless providing remarkably reliable estimates for the onset of global order. Here we expose that a spurious self-feedback effect, inherent to mean-field theory, underlies this apparent paradox. More specifically, we demonstrate that higher order interaction effects precisely cancel the self-feedback on the hubs, and we expose the importance of hubs for the distinct onset of local versus global order in the network. Due to the generic nature of our arguments, we expect the mechanism that we uncover for the archetypal case of Ising networks of the Barabási-Albert type to be also relevant for other systems with a strongly hierarchical underlying network structure.http://doi.org/10.1103/PhysRevResearch.3.033272 |
| spellingShingle | Claudia Merger Timo Reinartz Stefan Wessel Carsten Honerkamp Andreas Schuppert Moritz Helias Global hierarchy vs local structure: Spurious self-feedback in scale-free networks Physical Review Research |
| title | Global hierarchy vs local structure: Spurious self-feedback in scale-free networks |
| title_full | Global hierarchy vs local structure: Spurious self-feedback in scale-free networks |
| title_fullStr | Global hierarchy vs local structure: Spurious self-feedback in scale-free networks |
| title_full_unstemmed | Global hierarchy vs local structure: Spurious self-feedback in scale-free networks |
| title_short | Global hierarchy vs local structure: Spurious self-feedback in scale-free networks |
| title_sort | global hierarchy vs local structure spurious self feedback in scale free networks |
| url | http://doi.org/10.1103/PhysRevResearch.3.033272 |
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