scholarly journals Two betweenness centrality measures based on Randomized Shortest Paths

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
Ilkka Kivimäki ◽  
Bertrand Lebichot ◽  
Jari Saramäki ◽  
Marco Saerens
Keyword(s):  
Betweenness Centrality ◽  
Shortest Paths ◽  
Centrality Measures

scholarly journals Betweenness Centrality in Some Classes of Graphs

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Sunil Kumar Raghavan Unnithan ◽  
Balakrishnan Kannan ◽  
Madambi Jathavedan
Keyword(s):  
Real World ◽  
Betweenness Centrality ◽  
Shortest Paths ◽  
Centrality Measures ◽  
Flow Of Information

There are several centrality measures that have been introduced and studied for real-world networks. They account for the different vertex characteristics that permit them to be ranked in order of importance in the network. Betweenness centrality is a measure of the influence of a vertex over the flow of information between every pair of vertices under the assumption that information primarily flows over the shortest paths between them. In this paper we present betweenness centrality of some important classes of graphs.

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.

scholarly journals The Power of Quasi-Shortest Paths: $\rho$ -Geodesic Betweenness Centrality

2017 ◽  
Vol 4 (3) ◽  
pp. 187-200
Author(s):  
Dianne S. V. de Medeiros ◽  
Miguel Elias M. Campista ◽  
Nathalie Mitton ◽  
Marcelo Dias de Amorim ◽  
Guy Pujolle
Keyword(s):  
Betweenness Centrality ◽  
Shortest Paths

scholarly journals Betweenness centrality profiles in trees

2017 ◽  
Vol 5 (5) ◽  
pp. 776-794
Author(s):  
Benjamin Fish ◽  
Rahul Kushwaha ◽  
György Turán
Keyword(s):  
Betweenness Centrality ◽  
Shortest Paths ◽  
Random Trees ◽  
Experimental Results ◽  
Basic Notion ◽  
Worst Case ◽  
Scale Free ◽  
Order Of Magnitude

Abstract Betweenness centrality of a vertex in a graph measures the fraction of shortest paths going through the vertex. This is a basic notion for determining the importance of a vertex in a network. The $k$-betweenness centrality of a vertex is defined similarly, but only considers shortest paths of length at most $k$. The sequence of $k$-betweenness centralities for all possible values of $k$ forms the betweenness centrality profile of a vertex. We study properties of betweenness centrality profiles in trees. We show that for scale-free random trees, for fixed $k$, the expectation of $k$-betweenness centrality strictly decreases as the index of the vertex increases. We also analyse worst-case properties of profiles in terms of the distance of profiles from being monotone, and the number of times pairs of profiles can cross. This is related to whether $k$-betweenness centrality, for small values of $k$, may be used instead of having to consider all shortest paths. Bounds are given that are optimal in order of magnitude. We also present some experimental results for scale-free random trees.

From paths to blocks: New measures for street patterns

2016 ◽  
Vol 44 (2) ◽  
pp. 256-271 ◽  
Author(s):  
Marc Barthelemy
Keyword(s):  
Betweenness Centrality ◽  
Spatial Organization ◽  
Shortest Paths ◽  
Urban Systems ◽  
Conditional Probability Distribution ◽  
Planar Network ◽  
Formation And Evolution ◽  
Straight Lines ◽  
The Impact ◽  
Planar Networks

The street network is an important aspect of cities and contains crucial information about their organization and evolution. Characterizing and comparing various street networks could then be helpful for a better understanding of the mechanisms governing the formation and evolution of these systems. Their characterization is however not easy: there are no simple tools to classify planar networks and most of the measures developed for complex networks are not useful when space is relevant. Here, we describe recent efforts in this direction and new methods adapted to spatial networks. We will first discuss measures based on the structure of shortest paths, among which the betweenness centrality. In particular for time-evolving road networks, we will show that the spatial distribution of the betweenness centrality is able to reveal the impact of important structural transformations. Shortest paths are however not the only relevant ones. In particular, they can be very different from those with the smallest number of turns—the simplest paths. The statistical comparison of the lengths of the shortest and simplest paths provides a nontrivial and nonlocal information about the spatial organization of planar graphs. We define the simplicity index as the average ratio of these lengths and the simplicity profile characterizes the simplicity at different scales. Measuring these quantities on artificial (roads, highways, railways) and natural networks (leaves, insect wings) show that there are fundamental differences—probably related to their different function—in the organization of urban and biological systems: there is a clear hierarchy of the lengths of straight lines in biological cases, but they are randomly distributed in urban systems. The paths are however not enough to fully characterize the spatial pattern of planar networks such as streets and roads. Another promising direction is to analyze the statistics of blocks of the planar network. More precisely, we can use the conditional probability distribution of the shape factor of blocks with a given area, and define what could constitute the fingerprint of a city. These fingerprints can then serve as a basis for a classification of cities based on their street patterns. This method applied on more than 130 cities in the world leads to four broad families of cities characterized by different abundances of blocks of a certain area and shape. This classification will be helpful for identifying dominant mechanisms governing the formation and evolution of street patterns.

scholarly journals Ecological networks: Pursuing the shortest path, however narrow and crooked

2018 ◽  
Author(s):  
Andrea Costa ◽  
Ana M. Martín González ◽  
Katell Guizien ◽  
Andrea M. Doglioli ◽  
José María Gómez ◽  
...  
Keyword(s):  
Best Practices ◽  
Evolutionary Biology ◽  
Shortest Paths ◽  
Ecological Networks ◽  
Interaction Networks ◽  
Centrality Measures ◽  
Compact Representation ◽  
Sufficient Information ◽  
Ecological Data ◽  
Important Nodes

Representing data as networks cuts across all sub-disciplines in ecology and evolutionary biology. Besides providing a compact representation of the interconnections between agents, network analysis allows the identification of especially important nodes, according to various metrics that often rely on the calculation of the shortest paths connecting any two nodes. While the interpretation of a shortest paths is straightforward in binary, unweighted networks, whenever weights are reported, the calculation could yield unexpected results. We analyzed 129 studies of ecological networks published in the last decade and making use of shortest paths, and discovered a methodological inaccuracy related to the edge weights used to calculate shortest paths (and related centrality measures), particularly in interaction networks. Specifically, 49% of the studies do not report sufficient information on the calculation to allow their replication, and 61% of the studies on weighted networks may contain errors in how shortest paths are calculated. Using toy models and empirical ecological data, we show how to transform the data prior to calculation and illustrate the pitfalls that need to be avoided. We conclude by proposing a five-point check-list to foster best-practices in the calculation and reporting of centrality measures in ecology and evolution studies.

scholarly journals What makes a board director better connected? Evidence from graph theory

2020 ◽  
Vol 17 (2) ◽  
pp. 357-377
Author(s):  
Laleh Samarbakhsh ◽  
Boza Tasic
Keyword(s):  
Betweenness Centrality ◽  
Board Member ◽  
Centrality Measures ◽  
Board Members ◽  
Degree Centrality ◽  
Gender And Education ◽  
Board Directors ◽  
Board Director ◽  
High Level ◽  
The Impact

We are interested in quantifying and uncovering the relationships that form between the board directors of companies. Using these relationships we compute three network centrality measures for each director in the network and employ them in the analysis of connectedness of directors. Our focus in this study is on the attributes that make a board member better connected. The biological, educational and experiential attributes are used as independent variables to develop a regression model measuring the impact on the three connectivity measures (degree, betweenness and closeness). Our results show that ?Age? has a direct significant impact on all connectedness measures of a board member. We also find that female directors have a higher measure of degree centrality and betweenness centrality, but lower closeness. The number of foreign degrees increases the degree centrality and betweenness centrality but not closeness. The three identified characteristics of ?Age?, ?Gender?, and ?Education? are supporting the idea that a high level of social connection can in part be expected by the characteristics of individual board members and can explain up to 25% of the board member?s connectivity.

scholarly journals Forecasting failure locations in 2-dimensional disordered lattices

2019 ◽  
Vol 116 (34) ◽  
pp. 16742-16749 ◽  
Author(s):  
Estelle Berthier ◽  
Mason A. Porter ◽  
Karen E. Daniels
Keyword(s):  
Betweenness Centrality ◽  
Granular Media ◽  
Shortest Paths ◽  
Structural Materials ◽  
Geometric Structures ◽  
Contact Networks ◽  
Disordered Structure ◽  
Edge Betweenness ◽  
The Mean

Forecasting fracture locations in a progressively failing disordered structure is of paramount importance when considering structural materials. We explore this issue for gradual deterioration via beam breakage of 2-dimensional (2D) disordered lattices, which we represent as networks, for various values of mean degree. We study experimental samples with geometric structures that we construct based on observed contact networks in 2D granular media. We calculate geodesic edge betweenness centrality, which helps quantify which edges are on many shortest paths in a network, to forecast the failure locations. We demonstrate for the tested samples that, for a variety of failure behaviors, failures occur predominantly at locations that have larger geodesic edge betweenness values than the mean one in the structure. Because only a small fraction of edges have values above the mean, this is a relevant diagnostic to assess failure locations. Our results demonstrate that one can consider only specific parts of a system as likely failure locations and that, with reasonable success, one can assess possible failure locations of a structure without needing to study its detailed energetic states.

Better Understanding Network of Electrical Terminal Stations by Topological Analysis

2015 ◽  
Vol 804 ◽  
pp. 321-324
Author(s):  
Sunantha Sodsee ◽  
Maytiyanin Komkhao ◽  
Wolfgang A. Halang
Keyword(s):  
Power Transmission ◽  
Topological Analysis ◽  
Shortest Paths ◽  
Closeness Centrality ◽  
Centrality Measures ◽  
Theoretical Terms ◽  
The North ◽  
Electrical Terminal ◽  
Transmission Failures ◽  
Extreme Care

Preventing power transmission failures in its network of electrical terminal stations is a major concern for the infrastructure of the Thai capital Bangkok and its vicinity. Towards this objective the present study aims to analyse the network and its reliability under conditions of increased demand. The analysis is based on a representation of the network as a graph allowing to identify the most important terminal stations by graph-theoretical terms. These are, in particular, the centrality measures Degree Centrality (DC) giving the number of a station’s one-hop neighbours, Closeness Centrality (CC) describing the efficiency of power transmission from one station to others, shortest-path Betweenness Centrality (BC) indicating the number of a station’s occurrences on the shortest paths between indirectly connected stations, Hub describing stations that are connected to a large number of important stations, and Authority indicating the stations that connect many important stations. Experimental results revealed that the Bangkok Noi station was most significant when the measures DC, CC and BC were considered and, on the other hand, that the North Bangkok station was vital in terms of CC, Hub and Authority. Therefore, these stations need to be closely monitored and their operation to be carried out with extreme care in order to prevent the occurrence of power transmission failures within the Bangkok metropolitan area.

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