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 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 Identifying Node Importance in a Complex Network Based on Node Bridging Feature

2018 ◽  
Vol 8 (10) ◽  
pp. 1914 ◽  
Author(s):  
Lincheng Jiang ◽  
Yumei Jing ◽  
Shengze Hu ◽  
Bin Ge ◽  
Weidong Xiao
Keyword(s):  
Complex Networks ◽  
Large Scale ◽  
Shortest Paths ◽  
Evaluation Criteria ◽  
Local Network ◽  
Network Efficiency ◽  
Network Attack ◽  
Node Importance ◽  
Pass Through ◽  
Large Scale Networks

Identifying node importance in complex networks is of great significance to improve the network damage resistance and robustness. In the era of big data, the size of the network is huge and the network structure tends to change dynamically over time. Due to the high complexity, the algorithm based on the global information of the network is not suitable for the analysis of large-scale networks. Taking into account the bridging feature of nodes in the local network, this paper proposes a simple and efficient ranking algorithm to identify node importance in complex networks. In the algorithm, if there are more numbers of node pairs whose shortest paths pass through the target node and there are less numbers of shortest paths in its neighborhood, the bridging function of the node between its neighborhood nodes is more obvious, and its ranking score is also higher. The algorithm takes only local information of the target nodes, thereby greatly improving the efficiency of the algorithm. Experiments performed on real and synthetic networks show that the proposed algorithm is more effective than benchmark algorithms on the evaluation criteria of the maximum connectivity coefficient and the decline rate of network efficiency, no matter in the static or dynamic attack manner. Especially in the initial stage of attack, the advantage is more obvious, which makes the proposed algorithm applicable in the background of limited network attack cost.

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 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.

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 Faster Algorithms for Mining Shortest-Path Distances from Massive Time-Evolving Graphs

Algorithms ◽  
2020 ◽  
Vol 13 (8) ◽  
pp. 191
Author(s):  
Mattia D’Emidio
Keyword(s):  
Shortest Path ◽  
Real World ◽  
Large Scale ◽  
Web Search ◽  
Shortest Paths ◽  
Route Planning ◽  
Compact Representation ◽  
Worst Case ◽  
Evolving Graphs ◽  
Dynamic Algorithm

Computing shortest-path distances is a fundamental primitive in the context of graph data mining, since this kind of information is essential in a broad range of prominent applications, which include social network analysis, data routing, web search optimization, database design and route planning. Standard algorithms for shortest paths (e.g., Dijkstra’s) do not scale well with the graph size, as they take more than a second or huge memory overheads to answer a single query on the distance for large-scale graph datasets. Hence, they are not suited to mine distances from big graphs, which are becoming the norm in most modern application contexts. Therefore, to achieve faster query answering, smarter and more scalable methods have been designed, the most effective of them based on precomputing and querying a compact representation of the transitive closure of the input graph, called the 2-hop-cover labeling. To use such approaches in realistic time-evolving scenarios, when the managed graph undergoes topological modifications over time, specific dynamic algorithms, carefully updating the labeling as the graph evolves, have been introduced. In fact, recomputing from scratch the 2-hop-cover structure every time the graph changes is not an option, as it induces unsustainable time overheads. While the state-of-the-art dynamic algorithm to update a 2-hop-cover labeling against incremental modifications (insertions of arcs/vertices, arc weights decreases) offers very fast update times, the only known solution for decremental modifications (deletions of arcs/vertices, arc weights increases) is still far from being considered practical, as it requires up to tens of seconds of processing per update in several prominent classes of real-world inputs, as experimentation shows. In this paper, we introduce a new dynamic algorithm to update 2-hop-cover labelings against decremental changes. We prove its correctness, formally analyze its worst-case performance, and assess its effectiveness through an experimental evaluation employing both real-world and synthetic inputs. Our results show that it improves, by up to several orders of magnitude, upon average update times of the only existing decremental algorithm, thus representing a step forward towards real-time distance mining in general, massive time-evolving graphs.

A New Evaluation Method of Node Importance in Directed Weighted Complex Networks

2017 ◽  
Vol 5 (4) ◽  
pp. 367-375 ◽  
Author(s):  
Yu Wang ◽  
Jinli Guo ◽  
Han Liu
Keyword(s):  
Complex Networks ◽  
Complex Network ◽  
Real World ◽  
Evaluation Method ◽  
Network Models ◽  
Node Importance ◽  
Weighted Complex Network ◽  
Complex Network Models ◽  
Evaluation Matrix ◽  
Key Nodes

AbstractCurrent researches on node importance evaluation mainly focus on undirected and unweighted networks, which fail to reflect the real world in a comprehensive and objective way. Based on directed weighted complex network models, the paper introduces the concept of in-weight intensity of nodes and thereby presents a new method to identify key nodes by using an importance evaluation matrix. The method not only considers the direction and weight of edges, but also takes into account the position importance of nodes and the importance contributions of adjacent nodes. Finally, the paper applies the algorithm to a microblog-forwarding network composed of 34 users, then compares the evaluation results with traditional methods. The experiment shows that the method proposed can effectively evaluate the node importance in directed weighted networks.

scholarly journals The idemetric property: when most distances are (almost) the same

2019 ◽  
Vol 475 (2222) ◽  
pp. 20180283
Author(s):  
George Barmpalias ◽  
Neng Huang ◽  
Andrew Lewis-Pye ◽  
Angsheng Li ◽  
Xuechen Li ◽  
...  
Keyword(s):  
High Probability ◽  
Common Property ◽  
Shortest Paths ◽  
Network Models ◽  
Small World ◽  
Small World Network ◽  
Worst Case ◽  
Negative Results ◽  
Decentralized Algorithms ◽  
Wide Range

We introduce the idemetric property, which formalizes the idea that most nodes in a graph have similar distances between them, and which turns out to be quite standard amongst small-world network models. Modulo reasonable sparsity assumptions, we are then able to show that a strong form of idemetricity is actually equivalent to a very weak expander condition (PUMP). This provides a direct way of providing short proofs that small-world network models such as the Watts-Strogatz model are strongly idemetric (for a wide range of parameters), and also provides further evidence that being idemetric is a common property. We then consider how satisfaction of the idemetric property is relevant to algorithm design. For idemetric graphs, we observe, for example, that a single breadth-first search provides a solution to the all-pairs shortest paths problem, so long as one is prepared to accept paths which are of stretch close to 2 with high probability. Since we are able to show that Kleinberg's model is idemetric, these results contrast nicely with the well known negative results of Kleinberg concerning efficient decentralized algorithms for finding short paths: for precisely the same model as Kleinberg's negative results hold, we are able to show that very efficient (and decentralized) algorithms exist if one allows for reasonable preprocessing. For deterministic distributed routing algorithms we are also able to obtain results proving that less routing information is required for idemetric graphs than in the worst case in order to achieve stretch less than 3 with high probability: while Ω ( n 2 ) routing information is required in the worst case for stretch strictly less than 3 on almost all pairs, for idemetric graphs the total routing information required is O ( n log( n )).

GFT centrality: A new node importance measure for complex networks

2017 ◽  
Vol 487 ◽  
pp. 185-195 ◽  
Author(s):  
Rahul Singh ◽  
Abhishek Chakraborty ◽  
B.S. Manoj
Keyword(s):  
Complex Networks ◽  
Importance Measure ◽  
Node Importance

scholarly journals Ranking the spreading influence of nodes in complex networks based on mixing degree centrality and local structure

2019 ◽  
Vol 33 (32) ◽  
pp. 1950395 ◽  
Author(s):  
Pengli Lu ◽  
Chen Dong
Keyword(s):  
Complex Networks ◽  
Real World ◽  
Local Structure ◽  
Sir Model ◽  
Degree Centrality ◽  
Excellent Performance ◽  
H Index ◽  
Evaluation Standard ◽  
Node Importance ◽  
Key Nodes

The safety and robustness of the network have attracted the attention of people from all walks of life, and the damage of several key nodes will lead to extremely serious consequences. In this paper, we proposed the clustering H-index mixing (CHM) centrality based on the H-index of the node itself and the relative distance of its neighbors. Starting from the node itself and combining with the topology around the node, the importance of the node and its spreading capability were determined. In order to evaluate the performance of the proposed method, we use Susceptible–Infected–Recovered (SIR) model, monotonicity and resolution as the evaluation standard of experiment. Experimental results in artificial networks and real-world networks show that CHM centrality has excellent performance in identifying node importance and its spreading capability.

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