scholarly journals On the betweenness centrality of trees, forests and cycles

2018 ◽  
Vol 1 (4) ◽  
Author(s):  
Thomas Britz
Keyword(s):  
Betweenness Centrality ◽  
Mathematical Expressions

Simple mathematical expressions are given for the betweenness centrality of nodes in trees, forests and cycles. As application, a centrality test is given for when a network might be a forest.

scholarly journals Interdependence of friction, wear, and noise: A review

Friction ◽  
2021 ◽  
Author(s):  
Kevin Lontin ◽  
Muhammad Khan
Keyword(s):  
Mathematical Models ◽  
Friction And Wear ◽  
Review Paper ◽  
Acoustic Noise ◽  
Friction Noise ◽  
Mathematical Expressions ◽  
Mechanical Contacts ◽  
Exact Relationship ◽  
Modelling Approach ◽  
Frictional Noise

AbstractPhenomena of friction, wear, and noise in mechanical contacts are particularly important in the field of tribomechanics but equally complex if one wants to represent their exact relationship with mathematical models. Efforts have been made to describe these phenomena with different approaches in past. These efforts have been compiled in different reviews but most of them treated friction, wear mechanics, and acoustic noise separately. However, an in-depth review that provides a critical analysis on their interdependencies is still missing. In this review paper, the interdependencies of friction, wear, and noise are analysed in the mechanical contacts at asperitical level. The origin of frictional noise, its dependencies on contact’s mechanical properties, and its performance under different wear conditions are critically reviewed. A discussion on the existing mathematical models of friction and wear is also provided in the last section that leads to uncover the gap in the existing literature. This review concludes that still a comprehensive analytical modelling approach is required to relate the interdependencies of friction, noise, and wear with mathematical expressions.

Articulation points guided redundancy elimination for betweenness centrality

2016 ◽  
Vol 51 (8) ◽  
pp. 1-13 ◽  
Author(s):  
Lei Wang ◽  
Fan Yang ◽  
Liangji Zhuang ◽  
Huimin Cui ◽  
Fang Lv ◽  
...  
Keyword(s):  
Betweenness Centrality ◽  
Redundancy Elimination

scholarly journals Betweenness centrality for temporal multiplexes

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Silvia Zaoli ◽  
Piero Mazzarisi ◽  
Fabrizio Lillo
Keyword(s):  
Information Flow ◽  
Real World ◽  
Betweenness Centrality ◽  
Temporal Structure ◽  
Shortest Paths ◽  
Single Layer ◽  
Distance Metric ◽  
Definition Of

AbstractBetweenness centrality quantifies the importance of a vertex for the information flow in a network. The standard betweenness centrality applies to static single-layer networks, but many real world networks are both dynamic and made of several layers. We propose a definition of betweenness centrality for temporal multiplexes. This definition accounts for the topological and temporal structure and for the duration of paths in the determination of the shortest paths. We propose an algorithm to compute the new metric using a mapping to a static graph. We apply the metric to a dataset of $$\sim 20$$ ∼ 20 k European flights and compare the results with those obtained with static or single-layer metrics. The differences in the airports rankings highlight the importance of considering the temporal multiplex structure and an appropriate distance metric.

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