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 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

ParTBC: Faster Estimation of Top- k Betweenness Centrality Vertices on GPU

2022 ◽  
Vol 27 (2) ◽  
pp. 1-25
Author(s):  
Somesh Singh ◽  
Tejas Shah ◽  
Rupesh Nasre
Keyword(s):  
Network Analysis ◽  
Real World ◽  
Betweenness Centrality ◽  
Biological Network ◽  
State Of The Art ◽  
Shortest Paths ◽  
Weighted Graphs ◽  
Content Type ◽  
Practical Applications ◽  
Biological Network Analysis

Betweenness centrality (BC) is a popular centrality measure, based on shortest paths, used to quantify the importance of vertices in networks. It is used in a wide array of applications including social network analysis, community detection, clustering, biological network analysis, and several others. The state-of-the-art Brandes’ algorithm for computing BC has time complexities of and for unweighted and weighted graphs, respectively. Brandes’ algorithm has been successfully parallelized on multicore and manycore platforms. However, the computation of vertex BC continues to be time-consuming for large real-world graphs. Often, in practical applications, it suffices to identify the most important vertices in a network; that is, those having the highest BC values. Such applications demand only the top vertices in the network as per their BC values but do not demand their actual BC values. In such scenarios, not only is computing the BC of all the vertices unnecessary but also exact BC values need not be computed. In this work, we attempt to marry controlled approximations with parallelization to estimate the k -highest BC vertices faster, without having to compute the exact BC scores of the vertices. We present a host of techniques to determine the top- k vertices faster , with a small inaccuracy, by computing approximate BC scores of the vertices. Aiding our techniques is a novel vertex-renumbering scheme to make the graph layout more structured , which results in faster execution of parallel Brandes’ algorithm on GPU. Our experimental results, on a suite of real-world and synthetic graphs, show that our best performing technique computes the top- k vertices with an average speedup of 2.5× compared to the exact parallel Brandes’ algorithm on GPU, with an error of less than 6%. Our techniques also exhibit high precision and recall, both in excess of 94%.

scholarly journals Centralities for networks with consumable resources

2019 ◽  
Vol 7 (3) ◽  
pp. 376-401
Author(s):  
Hayato Ushijima-Mwesigwa ◽  
Zadid Khan ◽  
Mashrur A. Chowdhury ◽  
Ilya Safro
Keyword(s):  
Random Walk ◽  
Real World ◽  
Shortest Paths ◽  
Information Loss ◽  
Centrality Measures ◽  
Spreading Process ◽  
Social Actors ◽  
Simulation Based ◽  
Influential Nodes ◽  
Highly Correlated

AbstractIdentification of influential nodes is an important step in understanding and controlling the dynamics of information, traffic, and spreading processes in networks. As a result, a number of centrality measures have been proposed and used across different application domains. At the heart of many of these measures lies an assumption describing the manner in which traffic (of information, social actors, particles, etc.) flows through the network. For example, some measures only count shortest paths while others consider random walks. This paper considers a spreading process in which a resource necessary for transit is partially consumed along the way while being refilled at special nodes on the network. Examples include fuel consumption of vehicles together with refueling stations, information loss during dissemination with error-correcting nodes, and consumption of ammunition of military troops while moving. We propose generalizations of the well-known measures of betweenness, random-walk betweenness, and Katz centralities to take such a spreading process with consumable resources into account. In order to validate the results, experiments on real-world networks are carried out by developing simulations based on well-known models such as Susceptible-Infected-Recovered and congestion with respect to particle hopping from vehicular flow theory. The simulation-based models are shown to be highly correlated with the proposed centrality measures.Reproducibility: Our code and experiments are available at https://github.com/hmwesigwa/soc_centrality

scholarly journals Approximation of Interactive Betweenness Centrality in Large Complex Networks

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Sebastian Wandelt ◽  
Xing Shi ◽  
Xiaoqian Sun
Keyword(s):  
Complex Networks ◽  
Real World ◽  
Betweenness Centrality ◽  
Shortest Paths ◽  
Importance Measure ◽  
Worst Case ◽  
Approximation Techniques ◽  
Computational Costs ◽  
Node Importance ◽  
Wide Range

The analysis of real-world systems through the lens of complex networks often requires a node importance function. While many such views on importance exist, a frequently used global node importance measure is betweenness centrality, quantifying the number of times a node occurs on all shortest paths in a network. This centrality of nodes often significantly depends on the presence of nodes in the network; once a node is missing, e.g., due to a failure, other nodes’ centrality values can change dramatically. This observation is, for instance, important when dismantling a network: instead of removing the nodes in decreasing order of their static betweenness, recomputing the betweenness after a removal creates tremendously stronger attacks, as has been shown in recent research. This process is referred to as interactive betweenness centrality. Nevertheless, very few studies compute the interactive betweenness centrality, given its high computational costs, a worst-case runtime complexity of O(N∗∗4) in the number of nodes in the network. In this study, we address the research questions, whether approximations of interactive betweenness centrality can be obtained with reduction of computational costs and how much quality/accuracy needs to be traded in order to obtain a significant reduction. At the heart of our interactive betweenness approximation framework, we use a set of established betweenness approximation techniques, which come with a wide range of parameter settings. Given that we are interested in the top-ranked node(s) for interactive dismantling, we tune these methods accordingly. Moreover, we explore the idea of batch removal, where groups of top-k ranked nodes are removed before recomputation of betweenness centrality values. Our experiments on real-world and random networks show that specific variants of the approximate interactive betweenness framework allow for a speedup of two orders of magnitude, compared to the exact computation, while obtaining near-optimal results. This work contributes to the analysis of complex network phenomena, with a particular focus on obtaining scalable techniques.

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

SARCP - Exploiting Cyber-Attack Prediction Through Socially-Aware Recommendation

2022 ◽  
Vol 14 (1) ◽  
pp. 0-0
Keyword(s):  
Social Network ◽  
Real World ◽  
Cyber Security ◽  
Betweenness Centrality ◽  
Cyber Attacks ◽  
Experimental Results ◽  
Cyber Attack ◽  
Defence Mechanisms ◽  
Network Measure ◽  
Recommender Algorithm

In the domain of cyber security, the defence mechanisms of networks has traditionally been placed in a reactionary role. Cyber security professionals are therefore disadvantaged in a cyber-attack situation due to the fact that it is vital that they maneuver such attacks before the network is totally compromised. In this paper, we utilize the Betweenness Centrality network measure (social property) to discover possible cyber-attack paths and then employ computation of similar personality of nodes/users to generate predictions about possible attacks within the network. Our method proposes a social recommender algorithm called socially-aware recommendation of cyber-attack paths (SARCP), as an attack predictor in the cyber security defence domain. In a social network, SARCP exploits and delivers all possible paths which can result in cyber-attacks. Using a real-world dataset and relevant evaluation metrics, experimental results in the paper show that our proposed method is favorable and effective.

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.

scholarly journals Spatio-temporal networks: reachability, centrality and robustness

2016 ◽  
Vol 3 (6) ◽  
pp. 160196 ◽  
Author(s):  
Matthew J. Williams ◽  
Mirco Musolesi
Keyword(s):  
Real World ◽  
Failure Modes ◽  
Urban Transport ◽  
Transport Systems ◽  
Centrality Measures ◽  
Complex Nature ◽  
Temporal Networks ◽  
World Systems ◽  
Temporal System ◽  
Spatio Temporal

Recent advances in spatial and temporal networks have enabled researchers to more-accurately describe many real-world systems such as urban transport networks. In this paper, we study the response of real-world spatio-temporal networks to random error and systematic attack, taking a unified view of their spatial and temporal performance. We propose a model of spatio-temporal paths in time-varying spatially embedded networks which captures the property that, as in many real-world systems, interaction between nodes is non-instantaneous and governed by the space in which they are embedded. Through numerical experiments on three real-world urban transport systems, we study the effect of node failure on a network's topological, temporal and spatial structure. We also demonstrate the broader applicability of this framework to three other classes of network. To identify weaknesses specific to the behaviour of a spatio-temporal system, we introduce centrality measures that evaluate the importance of a node as a structural bridge and its role in supporting spatio-temporally efficient flows through the network. This exposes the complex nature of fragility in a spatio-temporal system, showing that there is a variety of failure modes when a network is subject to systematic attacks.

Efficient weighting strategy for enhancing synchronizability of complex networks

2018 ◽  
Vol 32 (11) ◽  
pp. 1850128 ◽  
Author(s):  
Youquan Wang ◽  
Feng Yu ◽  
Shucheng Huang ◽  
Juanjuan Tu ◽  
Yan Chen
Keyword(s):  
Complex Networks ◽  
Structural Properties ◽  
Real World ◽  
Centrality Measures ◽  
Node Degree ◽  
Scale Free ◽  
High Propensity ◽  
Network Link ◽  
Weighting Strategy ◽  
Weighting Methods

Networks with high propensity to synchronization are desired in many applications ranging from biology to engineering. In general, there are two ways to enhance the synchronizability of a network: link rewiring and/or link weighting. In this paper, we propose a new link weighting strategy based on the concept of the neighborhood subgroup. The neighborhood subgroup of a node i through node j in a network, i.e. [Formula: see text], means that node u belongs to [Formula: see text] if node u belongs to the first-order neighbors of j (not include i). Our proposed weighting schema used the local and global structural properties of the networks such as the node degree, betweenness centrality and closeness centrality measures. We applied the method on scale-free and Watts–Strogatz networks of different structural properties and show the good performance of the proposed weighting scheme. Furthermore, as model networks cannot capture all essential features of real-world complex networks, we considered a number of undirected and unweighted real-world networks. To the best of our knowledge, the proposed weighting strategy outperformed the previously published weighting methods by enhancing the synchronizability of these real-world networks.

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