Network descriptors based on betweenness centrality and transmission and their extremal values
Damir Vukičević,Gilles Caporossi +1 more
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TLDR
A series of network descriptors based on betweenness centrality and transmission are proposed and their extremal values as well as some graphs to which they correspond are given.About:
This article is published in Discrete Applied Mathematics.The article was published on 2013-11-01 and is currently open access. It has received 15 citations till now. The article focuses on the topics: Betweenness centrality & Random walk closeness centrality.read more
Citations
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Variable Neighborhood Search for extremal vertices
TL;DR: The main difference in this version of AutoGraphiX-III is that it aims at studying quantities that are related to vertices instead of invariants, which implies a complete change in the optimization algorithm that now natively handles multi objective optimization problems involving vertex-related measures.
Variable Neighborhood Search for Extremal Graphs 28: AutoGraphiX After Fifteen Years
TL;DR: The AutoGraphiX (AGX) system as discussed by the authors exploits different techniques from Variable Neighborhood Search to find extremal graphs, with respect to the maximization or minimization of a graph invariant, and then uses them for generating conjectures.
Variable neighborhood search for extremal vertices: The system AutoGraphiX-III
TL;DR: A third version of the AutoGraphiX software is made available, which now natively handles multiobjective problems involving vertex-related measures and is designed to help researchers in the field of complex networks.
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Minimum status of trees with given parameters
Zhene Peng,Bo Zhou +1 more
TL;DR: This work gives the smallest and largest values for the minimum status of a tree with fixed parameters such as the diameter, the number of pendant vertices, the numbers of odd vertices and the numberof vertices of degree two, and characterize the unique extremal trees.
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A Criticality Assessment Method for Power Transmission Lines in Power System
Wen Ying Liu,Cai Liang +1 more
TL;DR: Analytic Hierarchy Process (AHP) is presented in this article to measure the relative criticality for transmission lines, considering the changes of power system's status about transmission lines overload, central buses voltage over-limit and transient stability.
References
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Community structure in social and biological networks
Michelle Girvan,Mark Newman +1 more
TL;DR: This article proposes a method for detecting communities, built around the idea of using centrality indices to find community boundaries, and tests it on computer-generated and real-world graphs whose community structure is already known and finds that the method detects this known structure with high sensitivity and reliability.
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A Set of Measures of Centrality Based on Betweenness
TL;DR: A family of new measures of point and graph centrality based on early intuitions of Bavelas (1948) is introduced in this paper, which define centrality in terms of the degree to which a point falls on the shortest path between others and there fore has a potential for control of communication.
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Proximity and remoteness in graphs: Results and conjectures
Mustapha Aouchiche,Pierre Hansen +1 more
TL;DR: In this article, the authors proved upper and lower bounds on π and ρ as a function of the order n of a connected graph and compared them to the diameter, radius, average eccentricity, average distance, independence number and matching number.
Proximity and Remoteness in Graphs: Results and Conjectures
Mustapha Aouchiche,Pierre Hansen +1 more
TL;DR: Upper and lower bounds on π and ρ as a function of the order n of G are proved and a comparison between these two invariants follows and each one is compared to the diameter, radius, average eccentricity, average distance, independence number and matching number.