Studying node centrality based on the hidden hyperbolic metric space of complex networks

2019 ◽  
Vol 514 ◽  
pp. 426-434
Author(s):  
Lili Ma
Keyword(s):  
Complex Networks ◽  
Metric Space ◽  
Hyperbolic Metric ◽  
Node Centrality ◽  
Hyperbolic Metric Space

COUNTING CONJUGACY CLASSES IN

2018 ◽  
Vol 97 (3) ◽  
pp. 412-421
Author(s):  
MICHAEL HULL ◽  
ILYA KAPOVICH
Keyword(s):  
Cayley Graph ◽  
Metric Space ◽  
Hyperbolic Metric ◽  
Conjugacy Classes ◽  
Finitely Generated ◽  
Finitely Generated Group ◽  
Irreducible Elements ◽  
Hyperbolic Metric Space

We show that if a finitely generated group$G$has a nonelementary WPD action on a hyperbolic metric space$X$, then the number of$G$-conjugacy classes of$X$-loxodromic elements of$G$coming from a ball of radius$R$in the Cayley graph of$G$grows exponentially in$R$. As an application we prove that for$N\geq 3$the number of distinct$\text{Out}(F_{N})$-conjugacy classes of fully irreducible elements$\unicode[STIX]{x1D719}$from an$R$-ball in the Cayley graph of$\text{Out}(F_{N})$with$\log \unicode[STIX]{x1D706}(\unicode[STIX]{x1D719})$of the order of$R$grows exponentially in$R$.

scholarly journals Approximation of Endpoints for α—Reich–Suzuki Nonexpansive Mappings in Hyperbolic Metric Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1692
Author(s):  
Izhar Uddin ◽  
Sajan Aggarwal ◽  
Afrah A. N. Abdou
Keyword(s):  
Fixed Point ◽  
Convergence Analysis ◽  
Metric Space ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Hyperbolic Metric ◽  
Convergence Theorems ◽  
Hyperbolic Metric Space

The concept of an endpoint is a relatively new concept compared to the concept of a fixed point. The aim of this paper is to perform a convergence analysis of M—iteration involving α—Reich–Suzuki nonexpansive mappings. In this paper, we prove strong and Δ—convergence theorems in a hyperbolic metric space. Thus, our results generalize and improve many existing results.

Temporal node centrality in complex networks

2012 ◽  
Vol 85 (2) ◽  
Author(s):  
Hyoungshick Kim ◽  
Ross Anderson
Keyword(s):  
Complex Networks ◽  
Node Centrality

scholarly journals Analysis of the effect of node centrality on diffusion mode in complex networks

2017 ◽  
Vol 66 (12) ◽  
pp. 120201
Author(s):  
Su Zhen ◽  
Gao Chao ◽  
Li Xiang-Hua
Keyword(s):  
Complex Networks ◽  
Diffusion Mode ◽  
Node Centrality

scholarly journals TIME CENTRALITY IN DYNAMIC COMPLEX NETWORKS

2015 ◽  
Vol 18 (07n08) ◽  
pp. 1550023 ◽  
Author(s):  
EDUARDO C. COSTA ◽  
ALEX B. VIEIRA ◽  
KLAUS WEHMUTH ◽  
ARTUR ZIVIANI ◽  
ANA PAULA COUTO DA SILVA
Keyword(s):  
Diffusion Process ◽  
Complex Networks ◽  
Diffusion Processes ◽  
Temporal Evolution ◽  
Dynamic Network ◽  
Time Varying ◽  
Relative Importance ◽  
Node Centrality ◽  
Centrality Metrics ◽  
Efficient Diffusion

There is an ever-increasing interest in investigating dynamics in time-varying graphs (TVGs). Nevertheless, so far, the notion of centrality in TVG scenarios usually refers to metrics that assess the relative importance of nodes along the temporal evolution of the dynamic complex network. For some TVG scenarios, however, more important than identifying the central nodes under a given node centrality definition is identifying the key time instants for taking certain actions. In this paper, we thus introduce and investigate the notion of time centrality in TVGs. Analogously to node centrality, time centrality evaluates the relative importance of time instants in dynamic complex networks. In this context, we present two time centrality metrics related to diffusion processes. We evaluate the two defined metrics using both a real-world dataset representing an in-person contact dynamic network and a synthetically generated randomized TVG. We validate the concept of time centrality showing that diffusion starting at the best ranked time instants (i.e., the most central ones), according to our metrics, can perform a faster and more efficient diffusion process.

scholarly journals Approximating Fixed Points of Reich–Suzuki Type Nonexpansive Mappings in Hyperbolic Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Kifayat Ullah ◽  
Junaid Ahmad ◽  
Manuel De La Sen ◽  
Muhammad Naveed Khan
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Iterative Process ◽  
Fixed Point Theory ◽  
Nonexpansive Mappings ◽  
Point Theory ◽  
Hyperbolic Spaces ◽  
Uniformly Convex ◽  
Convergence Results ◽  
Hyperbolic Metric Space

In this work, we prove some strong and Δ convergence results for Reich-Suzuki type nonexpansive mappings through M iterative process. A uniformly convex hyperbolic metric space is used as underlying setting for our approach. We also provide an illustrate numerical example. Our results improve and extend some recently announced results of the metric fixed-point theory.

Cercles De Remplissage and Asymptotic Behaviour along Circuitous Paths

1970 ◽  
Vol 22 (2) ◽  
pp. 389-393 ◽  
Author(s):  
P. M. Gauthier
Keyword(s):  
Meromorphic Function ◽  
Asymptotic Behaviour ◽  
Metric Space ◽  
Unit Disc ◽  
Riemann Sphere ◽  
Holomorphic Functions ◽  
Weak Form ◽  
Value Distribution ◽  
Hyperbolic Metric ◽  
Chordal Metric

In this paper we consider the value distribution of a meromorphic function whose behaviour is prescribed along a spiral. The existence of extremely wild holomorphic functions is established. Indeed a very weak form of one of our results would be that there are holomorphic functions (in the unit disc or the plane) for which every curve “tending to the boundary” is a Julia curve.The theorems in this paper generalize results of Gavrilov [7], Lange [9], and Seidel [11].I wish to express my thanks to Professor W. Seidel for his guidance and encouragement.2. Preliminaries. For the most part we will be dealing with the metric space (D, ρ) where D is the unit disc, |z| < 1, and ρ is the non-Euclidean hyperbolic metric on D. The chordal metric on the Riemann sphere will be denoted by x.

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