Routes Obey Hierarchy in Complex Networks

Csoma, Attila; Kő̈rösi, Attila; Rétvári, Gábor; Heszberger, Zalán; Bı́ró, József; Slíz, Mariann; Avena-Koenigsberger, Andrea; Griffa, Alessandra; Hagmann, Patric; Gulyás, András

doi:10.1038/s41598-017-07412-4

Cited by 12 publications

(12 citation statements)

References 21 publications

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“…Gao et al showed that the paths of packets going through the internet are also detoured in a non-negligible extent 30 and they show that the hierarchical policies of internet packet routing may be responsible for the major proportion of the inflation. Detours have been identified in road networks by Zhu et al 31 and in cattle pen systems by Grandin 32 , while similar phenomena was reported in airport 10,27 and brain networks 10,33 too.…”

Section: Introductionmentioning

confidence: 55%

“…traveling between locations in a city using public transportation). The available navigational datasets [1][2][3][4] and models [3][4][5][6][7][8][9][10] considering networked systems, mostly target to uncover the average properties of a group of subjects and capture collective human behavior. Thus existing datasets do not have sufficient data or appropriate tracing methods permitting the analysis of long-term individual patterns.…”

Section: Introductionmentioning

confidence: 99%

“…As a result, real paths will be somewhat longer than the shortest alternatives, but the detours will be characteristic to the individual taking them, as no two may abstract away the same hierarchy of the network. Although there are existing models assuming latent hierarchical scaffolds aiding navigation 6,10,[16][17][18][19] , this is the first study processing sufficient individual human navigation data to visualize and analyse these individually created hierarchies.…”

Section: Introductionmentioning

confidence: 99%

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The role of detours in individual human navigation patterns of complex networks

Gulyás¹,

Bı́ró²,

Rétvári³

et al. 2019

Preprint

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Despite their importance for public transportation, communication within organizations or the general understanding of organized knowledge, our understanding of how human individuals navigate in complex networked systems is still limited owing to the lack of datasets recording sufficient amount of navigation paths of individual humans. Here, we analyze 10587 paths recorded from 259 human subjects when navigating between nodes of a complex word-morph network. We find the clear presence of systematic detours organized around individual hierarchical scaffolds guiding navigation. Our dataset is the first enabling the visualization and analysis of scaffold hierarchies whose presence and role in supporting human navigation is assumed in existing navigational models. By using an information theoretic argumentation, we argue that taking short detours following the hierarchical scaffolds is a clear sign of human subjects simplifying the interpretation of the complex networked system by an order of magnitude. We also discuss the role of these scaffolds in the phases of learning to navigate a network from scratch.

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Section: Introductionmentioning

confidence: 55%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The role of detours in individual human navigation patterns of complex networks

Gulyás¹,

Bı́ró²,

Rétvári³

et al. 2019

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Gao et al showed that the paths of packets going through the internet are also detoured to a non-negligible extent 21 , and they showed that the hierarchical policies of internet packet routing may be responsible for a major proportion of the inflation. Detours have been identified in road networks by Zhu et al 22 and in cattle pen systems by Grandin 23 , while similar phenomena were also reported in airports 10,24 and brain networks 10,25 .…”

mentioning

confidence: 53%

“…As a result, real paths will be somewhat longer than the shortest alternatives, but the detours will be characteristic to the individual taking them, as no two individuals may abstract the same hierarchy of the network. Although there are existing models assuming latent hierarchical scaffolds aiding navigation 6,10,[17][18][19][20] , this is the first study processing sufficient individual human navigation data to visualize and analyse these individually created hierarchies.…”

mentioning

confidence: 99%

The role of detours in individual human navigation patterns of complex networks

Gulyás

Bı́ró

Rétvári

et al. 2020

Sci Rep

Self Cite

View full text Add to dashboard Cite

Despite its importance for public transportation, communication within organizations or the general understanding of organized knowledge, our understanding of how human individuals navigate complex networked systems is still limited owing to the lack of datasets recording a sufficient amount of navigation paths of individual humans. Here, we analyse 10587 paths recorded from 259 human subjects when navigating between nodes of a complex word-morph network. We find a clear presence of systematic detours organized around individual hierarchical scaffolds guiding navigation. Our dataset is the first enabling the visualization and analysis of scaffold hierarchies whose presence and role in supporting human navigation is assumed in existing navigational models. By using an informationtheoretic argumentation, we argue that taking short detours following the hierarchical scaffolds is a clear sign of human subjects simplifying the interpretation of the complex networked system by an order of magnitude. We also discuss the role of these scaffolds in the phases of learning to navigate a network from scratch. Everyday life is full of complex networked systems that humans recurringly navigate on a daily basis (e.g., travelling between locations in a city using public transportation). The available navigational datasets 1-4 and models 3-10 considering networked systems mostly target uncovering the average properties of a group of subjects and capture collective human behaviour. Moreover, in terms of human navigation, the existing experiments focus on the dynamic process of learning to navigate, i.e., how people incrementally learn an approximate map of the network. Thus, existing datasets do not have sufficient data or appropriate tracing methods permitting the analysis of long-term individual patterns. Here, we analyse the results of an experiment 11 with human subjects solving navigational tasks in a complex word-morph network. The recorded average of 40.9 timely ordered paths from 259 subjects and more than 200 paths from 9 subjects makes the analysis of individual human navigation patterns possible. In contrast to existing studies, this amount of data enables the inference of characteristics about the steady-state way in which people choose a path between endpoints of a network after they have learned how to navigate the network in their individual way. We argue that this routine navigation process is more valuable to investigate since people use this approach on a daily basis. In the remainder of this study, we refer to this steady-state navigation simply as human navigation. The nodes of the word-morph network, from which we process the navigation paths, are English words that are connected if they differ in only a single letter. In this large and complex network, human subjects are given navigational tasks, i.e., to reach a destination word from a starting word by changing only one letter at a time, while still having meaningful words in intermediate states. Figure 1a shows a sample fragment of the word-morph network an...

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