Asymptotic traffic flow in a hyperbolic network

Baryshnikov, Yuliy; Tucci, Gabriel H.

doi:10.1109/isccsp.2012.6217862

Cited by 8 publications

(18 citation statements)

References 13 publications

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“…In the study of communication networks, the core is usually identified by the small dense part that carries out most traffic under shortest path routing [5,24]. It is quite natural to associate the concepts of the network's core and its center.…”

Section: Theoretical Background and Related Workmentioning

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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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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Section: Theoretical Background and Related Workmentioning

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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“…The asymptotic traffic flow in hyperbolic graphs has been studied in Baryshnikov and Tucci. 25 It shows that a vertex v belongs to the core if there exists a finite radius r such that the amount of the traffic that passes through the ball centered at v and with radius r behaves asymptotically as (n 2 ) as the number of vertices n grows to infinity. The existence of the core in large networks such as the Internet motivates researchers to embed the Internet distance metric in a hyperbolic space for distance estimation.…”

Section: Core-periphery and Network Centrality In Complex Networkmentioning

confidence: 99%

“…It was suggested by Baryshnikov and Tucci 25 and Narayan and Saniee 6 that the highly congested cores in many communication networks can be due to their hyperbolicity or negative curvature. Those cores are represented by vertices that belong to most shortest paths (shortest-path betweenness centrality) and (or) have minimum distances to all other vertices (eccentricity centrality).…”

Section: Core-periphery Models Based On D-hyperbolicitymentioning

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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“…As a byproduct, we showed that the probability of a node having a load l scales as 1/l^2 in such models, a point of controversy prior to our work. A formal proof of O(N^2) scaling of load in δ-hyperbolic networks was subsequently furnished in [3,4,5].…”

Section: Project Accomplishmentsmentioning

confidence: 99%

An Analytical Framework for Fast Estimation of Capacity and Performance in Communication Networks

Saniee¹,

Baryshnikov²,

Narayan³

2012

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Asymptotic traffic flow in a hyperbolic network

Cited by 8 publications

References 13 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

An Analytical Framework for Fast Estimation of Capacity and Performance in Communication Networks

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