Topological implications of negative curvature for biological and social networks

Albert, Réka; DasGupta, Bhaskar; Mobasheri, Nasim

doi:10.1103/physreve.89.032811

Cited by 56 publications

(84 citation statements)

References 45 publications

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“…This confirms the results in [4]. However, unlike previous efforts, we analyze the relationship between the hyperbolicity and other global parameters of the graph.…”

Section: Introductionsupporting

confidence: 89%

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Core-Periphery Models for Graphs Based on their δ-Hyperbolicity: An Example Using Biological Networks

Alrasheed

Dragan

2015

Studies in Computational Intelligence

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Abstract. Hyperbolicity is a global property of graphs that measures how close their structures are to trees in terms of their distances. It embeds multiple properties that facilitate solving several problems that found to be hard in the general graph form. In this paper, we investigate the hyperbolicity of graphs not only by considering Gromov's notion of δ-hyperbolicity but also by analyzing its relationship to other graph's parameters. This new perspective allows us to classify graphs with respect to their hyperbolicity, and to show that many biological networks are hyperbolic. Then we introduce the eccentricity-based bending property which we exploit to identify the core vertices of a graph by proposing two models: the Maximum-Peak model and the Minimum Cover Set model.

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“…This confirms the results in [4]. However, unlike previous efforts, we analyze the relationship between the hyperbolicity and other global parameters of the graph.…”

Section: Introductionsupporting

confidence: 89%

“…Multiple complex networks such as the Internet [28,14], data networks at the IP layer [24], and social and biological networks [4,2] show low δ-hyperbolicity (low hyperbolicity suggests a structure that is close to a tree structure [14,3]). Also, it has been observed that networks with this property have highly connected cores [24].…”

Section: Introductionmentioning

confidence: 99%

Core-Periphery Models for Graphs Based on their δ-Hyperbolicity: An Example Using Biological Networks

Alrasheed

Dragan

2015

Studies in Computational Intelligence

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“…This forces the sides of the triangle to be curved toward its center as its size increases. 7 Multiple complex networks such as the Internet, 8,9 data networks at the IP layer, 6 and social and biological networks 10,11 show low -hyperbolicity (low hyperbolicity suggests a structure that is close to a tree structure 12 ). Also, it has been observed that networks with this property have highly connected cores.…”

Section: Introductionmentioning

confidence: 99%

Core–periphery models for graphs based on their δ-hyperbolicity: An example using biological networks

Alrasheed

Dragan

2016

Journal of Algorithms & Computational Technology

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Hyperbolicity is a global property of graphs that measures how close their structures are to trees in terms of their distances. It embeds multiple properties that facilitate solving several problems that found to be hard in the general graph form. In this paper, we investigate the hyperbolicity of graphs not only by considering Gromov's notion of -hyperbolicity but also by analyzing its relationship to other graph's parameters. This new perspective allows us to classify graphs with respect to their hyperbolicity and to show that many biological networks are hyperbolic. Then we introduce the eccentricity-based bending property which we exploit to identify the core vertices of a graph by proposing two models: the maximum-peak model and the minimum cover set model. In this extended version of the paper, we include some new theorems, as well as proofs of the theorems proposed in the conference paper. Also, we present the algorithms we used for each of the proposed core identification models, and we provide more analysis, explanations, and examples.

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“…In recent years, the notion of δ-hyperbolicity [22] has been generalized and studied in different types of networks [23][24][25][26][27][28]. It has been shown that the occurrence of negative curvature has implications on the navigability and dynamic processes in networks [29,30]. The issue of precise mechanisms is still open, perhaps depending on the type of dynamics.…”

Section: Introductionmentioning

confidence: 99%

Origin of Hyperbolicity in Brain-to-Brain Coordination Networks

Tadić¹,

Andjelković²,

Šuvakov³

2018

Front. Phys.

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Hyperbolicity or negative curvature of complex networks is the intrinsic geometric proximity of nodes in the graph metric space, which implies an improved network function. Here, we investigate hidden combinatorial geometries in brain-to-brain coordination networks arising through social communications. The networks originate from correlations among EEG signals previously recorded during spoken communications comprising of 14 individuals with 24 speaker-listener pairs. We find that the corresponding networks are δ-hyperbolic with δ max = 1 and the graph diameter D = 3 in each brain. While the emergent hyperbolicity in the two-brain networks varies satisfying δ max /D/2 ≤ 1 and can be attributed to the topology of the subgraph formed around the cross-brains linking channels. We identify these subgraphs in each studied two-brain network and decompose their structure into simple geometric descriptors (triangles, tetrahedra and cliques of higher orders) that contribute to hyperbolicity. Considering topologies that exceed two separate brain networks as a measure of coordination synergy between the brains, we identify different neural correlation patterns ranging from weak coordination to super-brain structure. These topology features are in qualitative agreement with the listener's self-reported ratings of own experience and quality of the speaker, suggesting that studies of the cross-brain connector networks can reveal new insight into the neural mechanisms underlying human social behavior.

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Topological implications of negative curvature for biological and social networks

Cited by 56 publications

References 45 publications

Core-Periphery Models for Graphs Based on their δ-Hyperbolicity: An Example Using Biological Networks

Core-Periphery Models for Graphs Based on their δ-Hyperbolicity: An Example Using Biological Networks

Core–periphery models for graphs based on their δ-hyperbolicity: An example using biological networks

Origin of Hyperbolicity in Brain-to-Brain Coordination Networks

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