Why Are There Six Degrees of Separation in a Social Network?

Samoylenko, Ivan; Aleja, David; Primo, E.; Alfaro-Bittner, K.; Vasilyeva, Ekaterina; Kovalenko, Kirill; Musatov, Daniil; Райгородский, А. М.; Criado, Regino; Romance, Miguel; Papo, David; Perc, Matjaž; Barzel, Baruch; Boccaletti, Stefano

doi:10.1103/physrevx.13.021032

Cited by 8 publications

(5 citation statements)

References 61 publications

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“…This approach follows similar studies in synthetic brain networks, where a work also using game theory showed how nodes aiming at maximizing the network’s navigability while minimizing their wiring cost organize in structures remarkably similar to empirical brain networks [5]. Interestingly, related work [64] addressed the long-standing question of why six degrees of separation exist in social networks [65]. Using normative modeling provided by game theory, the authors found the reason to be a trade-off between a node’s aspiration to maximize its centrality, while minimizing its connection maintenance cost [64].…”

Section: Discussionmentioning

confidence: 81%

“…Interestingly, related work [64] addressed the long-standing question of why six degrees of separation exist in social networks [65]. Using normative modeling provided by game theory, the authors found the reason to be a trade-off between a node’s aspiration to maximize its centrality, while minimizing its connection maintenance cost [64]. In the present work, we also found that the first eight steps of propagation are sufficient to reconstruct OI, with a peak on the sixth step.…”

Section: Discussionmentioning

confidence: 99%

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A General Framework for Characterizing Optimal Communication in Brain Networks

Fakhar,

Hadaeghi,

Seguin

et al. 2024

Preprint

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Communication in brain networks is the foundation of cognitive function and behavior. A multitude of evolutionary pressures, including the minimization of metabolic costs while maximizing communication efficiency, contribute to shaping the structure and dynamics of these networks. However, how communication efficiency is characterized depends on the assumed model of communication dynamics. Traditional models include shortest path signaling, random walker navigation, broadcasting, and diffusive processes. Yet, a general and model-agnostic framework for characterizing optimal neural communication remains to be established.Our study addresses this challenge by assigning communication efficiency through game theory, based on a combination of structural data from human cortical networks with computational models of brain dynamics. We quantified the exact influence exerted by each brain node over every other node using an exhaustive multi-site virtual lesioning scheme, creating optimal influence maps for various models of brain dynamics. These descriptions show how communication patterns unfold in the given brain network if regions maximize their influence over one another. By comparing these influence maps with a large variety of brain communication models, we found that optimal communication most closely resembles a broadcasting model in which regions leverage multiple parallel channels for information dissemination. Moreover, we show that the most influential regions within the cortex are formed by its rich-club. These regions exploit their topological vantage point by broadcasting across numerous pathways, thereby significantly enhancing their effective reach even when the anatomical connections are weak.Our work provides a rigorous and versatile framework for characterizing optimal communication across brain networks and reveals the most influential brain regions and the topological features underlying their optimal communication.

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Section: Discussionmentioning

confidence: 81%

Section: Discussionmentioning

confidence: 99%

A General Framework for Characterizing Optimal Communication in Brain Networks

Fakhar,

Hadaeghi,

Seguin

et al. 2024

Preprint

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“…Also, preferences for indirect utility can be considered even in connections between existing nodes for realistic extensions. A recent study shows that selection to increase betweenness centrality forms an ultra-small world network through a game theoretical framework 50 . Preferences for indirect utility are likely to make a similar contribution, as it could be a practical way to increase betweenness centrality.…”

Section: Discussionmentioning

confidence: 99%

Emergence of a mutual-growth mechanism in networks evolved by social preference based on indirect utility

Lee,

Ogawa

2023

Sci Rep

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Preferential attachment is an important mechanism in the structural evolution of complex networks. However, though resources on a network propagate and have an effect beyond a direct relationship, growth by preferential attachment based on indirectly propagated resources has not been systematically investigated. Here, we propose a mathematical model of an evolving network in which preference is proportional to a utility function reflecting direct utility from directly connected nodes and indirect utility from indirectly connected nodes beyond the directly connected nodes. Our analysis showed that preferential attachment involving indirect utility forms a converged and hierarchical structure, thereby significantly increasing the indirect utility across the entire network. Further, we found that the structures are formed by mutual growth between adjacent nodes, which promotes a scaling exponent of 1.5 between the number of indirect and direct links. Lastly, by examining several real networks, we found evidence of mutual growth, especially in social networks. Our findings demonstrate a growth mechanism emerging in evolving networks with preference for indirect utility, and provide a foundation for systematically investigating the role of preference for indirect utility in the structural and functional evolution of large-scale social networks.

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“…Winner-loser effects mildly reduce the average shortest path length over all pairs of nodes in small random networks, but they do not seem to significantly contribute to global network efficiency 17 , 18 . Random networks of any size show “small-world” features with “six degrees of separation” 15 , 26 , and thus, are already quite “efficient” in the sense of network theory. Winner-loser effects as simulated in this study, do not further reduce average path length over all pairs of nodes, but lead on the local level to substantial centralization.…”

Section: Discussionmentioning

confidence: 99%

Winner-loser effects improve social network efficiency between competitors with equal resource holding power

Hermanussen,

Dammhahn,

Scheffler

et al. 2023

Sci Rep

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Animal societies are structured of dominance hierarchy (DH). DH can be viewed as networks and analyzed by graph theory. We study the impact of state-dependent feedback (winner-loser effect) on the emergence of local dominance structures after pairwise contests between initially equal-ranking members (equal resource-holding-power, RHP) of small and large social groups. We simulated pairwise agonistic contests between individuals with and without a priori higher RHP by Monte-Carlo-method. Random pairwise contests between equal-ranking competitors result in random dominance structures (‘Null variant’) that are low in transitive triads and high in pass along triads; whereas state-dependent feedback (‘Winner-loser variant’) yields centralized ‘star’ structured DH that evolve from competitors with initially equal RHP and correspond to hierarchies that evolve from keystone individuals. Monte-Carlo simulated DH following state-dependent feedback show motif patterns very similar to those of a variety of natural DH, suggesting that state-dependent feedback plays a pivotal role in robust self-organizing phenomena that transcend the specifics of the individual. Self-organization based on state-dependent feedback leads to social structures that correspond to those resulting from pre-existing keystone individuals. As the efficiency of centralized social networks benefits both, the individual and the group, centralization of social networks appears to be an important evolutionary goal.

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Why Are There Six Degrees of Separation in a Social Network?

Cited by 8 publications

References 61 publications

A General Framework for Characterizing Optimal Communication in Brain Networks

A General Framework for Characterizing Optimal Communication in Brain Networks

Emergence of a mutual-growth mechanism in networks evolved by social preference based on indirect utility

Winner-loser effects improve social network efficiency between competitors with equal resource holding power

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