Hierarchical route to the emergence of leader nodes in real-world networks

O’Brien, Joseph D.; Oliveira, Kleber A.; Gleeson, James P.; Asllani, Malbor

doi:10.1103/physrevresearch.3.023117

Cited by 13 publications

(16 citation statements)

References 90 publications

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“…Finally, extending the model to consider individuals with different importance would be interesting. Some individuals might be more influential because of their status [25], reputation [26], or position in a hierarchical structure [27]. It would be straightforward to account for the importance of each individual when computing group majorities.…”

Section: Discussionmentioning

confidence: 99%

Fragmentation from group interactions: A higher-order adaptive voter model

Papanikolaou¹,

Lambiotte²,

Vaccario³

2023

Preprint

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The adaptive voter model allows for studying the interplay between homophily, the tendency of like-minded individuals to attract each other, and social influence, the tendency for connected individuals to influence each other. However, it relies on graphs, and thus, it only considers pairwise interactions. We develop a minimal extension of the adaptive voter model to hypergraphs to study the interactions of groups of arbitrary sizes using a threshold parameter. We study S-uniform hypergraphs as initial configurations. With numerical simulations, we find new phenomena not found in the counterpart pairwise models, such as the formation of bands in the magnetization and the lack of an equilibrium state. Finally, we develop an analytical model using a sparse hypergraph approximation that accurately predicts the bands' boundaries and height.

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Section: Discussionmentioning

confidence: 99%

Fragmentation from group interactions: A higher-order adaptive voter model

Papanikolaou¹,

Lambiotte²,

Vaccario³

2023

Preprint

View full text Add to dashboard Cite

show abstract

“…( 2) can be interpreted as a dynamical process on a complex network with non-normal M representing its adjacency matrix. Such non-normal networks have been observed in a wide variety of biological and soclo-economic networks [28,29], and their role in the transmission of noise has been studied [44]. Recall that asymmetry of M is a necessary, but not a sufficient condition for non-normality.…”

Section: Parametrization Of Non-normal Matrices With Level-dependent ...mentioning

confidence: 99%

“…Recently, new methods to generate non-normal networks have been proposed by taking into consideration asymmetrical reciprocity [28] and hierarchy [29] that are typical of non-normal systems. Drawing from these insights, we implement here an algorithm that allows us to control the rate of non-normality along with the number of top nodes, that can be interpreted as thought leaders.…”

Section: Parametrization Of Non-normal Matrices With Level-dependent ...mentioning

confidence: 99%

“…The non-normal network with a total of N nodes is initialized with N 0 so-called top nodes. These top nodes account for the largely independent N 0 backbones of the communication network common to typical hierarchically, non-normal networks [29]. The remaining N − N 0 nodes are added to the existing network sequentially, one node at a time.…”

Section: Parametrization Of Non-normal Matrices With Level-dependent ...mentioning

confidence: 99%

“…The adjacency matrix A should thus represent a hierarchy of asymmetric interactions [26,27]. Mathematically, this is represented by non-normal adjacency matrices A [28,29]. Analyzing Reddit discussion forums of meme stocks, we show that patterns of influence are highly non-normal, and that the rate of reciprocity is dependent on a user hierarchy.…”

mentioning

confidence: 97%

See 2 more Smart Citations

Non-Normal Interactions Create Socio-Economic Bubbles

Sornette¹,

Lera²,

Lin³

et al. 2022

SSRN Journal

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Two wrongs do not make a right: the assumption that an inhibitor acts as an inverse activator

Jayathilaka,

Araujo,

Nguyen

et al. 2024

J. Math. Biol.

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Models of biochemical networks are often large intractable sets of differential equations. To make sense of the complexity, relationships between genes/proteins are presented as connected graphs, the edges of which are drawn to indicate activation or inhibition relationships. These diagrams are useful for drawing qualitative conclusions in many cases by the identifying recurring of topological motifs, for example positive and negative feedback loops. These topological features are usually classified under the presumption that activation and inhibition are inverse relationships. For example, inhibition of an inhibitor is often classified the same as activation of an activator within a motif classification, effectively treating them as equivalent. Whilst in many contexts this may not lead to catastrophic errors, drawing conclusions about the behavior of motifs, pathways or networks from these broad classes of topological feature without adequate mathematical descriptions can lead to obverse outcomes. We investigate the extent to which a biochemical pathway/network will behave quantitatively dissimilar to pathway/ networks with similar typologies formed by swapping inhibitors as the inverse of activators. The purpose of the study is to determine under what circumstances rudimentary qualitative assessment of network structure can provide reliable conclusions as to the quantitative behaviour of the network. Whilst there are others, We focus on two main mathematical qualities which may cause a divergence in the behaviour of two pathways/networks which would otherwise be classified as similar; (i) a modelling feature we label ‘bias’ and (ii) the precise positioning of activators and inhibitors within simple pathways/motifs.

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Hierarchical route to the emergence of leader nodes in real-world networks

Cited by 13 publications

References 90 publications

Fragmentation from group interactions: A higher-order adaptive voter model

Fragmentation from group interactions: A higher-order adaptive voter model

Non-Normal Interactions Create Socio-Economic Bubbles

Two wrongs do not make a right: the assumption that an inhibitor acts as an inverse activator

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